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Journal articles on the topic 'LMI (linear matrix inequality)'

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Published: 4 June 2021

Last updated: 15 February 2022

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1

Wang, Hai Yan. "Linear Matrix Inequality and its Application in Control Theory." Advanced Materials Research 853 (December 2013): 636–40. http://dx.doi.org/10.4028/www.scientific.net/amr.853.636.

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As a result of linear matrix inequality (LMI) and its good nature of mathematics as well as the breakthrough of solution method, many control problems can be transformed into a standard LMI problem to solve. Linear matrix inequality has received widely attention and applications in control system analysis and design. This paper introduces some of the basic content of LMI, such as the general description, the relevant algorithms and software. The controller will be designed using LMI such that the closed-loop system is asymptotically stable, and simulation will be given using Matlab. Finally, the population model will be given and analyzed.

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2

Abdalla, M. O., K. M. Grigoriadis, and D. C. Zimmerman. "Structural Damage Detection Using Linear Matrix Inequality Methods." Journal of Vibration and Acoustics 122, no. 4 (2000): 448–55. http://dx.doi.org/10.1115/1.1287029.

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In this work, linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of stiffness reduction in structures using experimental modal data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved efficiently using recently developed interior-point methods. Both a matrix update and a parameter update formulation of the damage detection is provided in terms of LMIs. The presence of noise in the experimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered beam test-bed using experimental data obtained from modal tests. [S0739-3717(00)00104-5]

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3

Zhang, Hui. "The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities." Applied Mechanics and Materials 192 (July 2012): 406–11. http://dx.doi.org/10.4028/www.scientific.net/amm.192.406.

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Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

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4

Pai, Neng-Sheng, and Her-Terng Yau. "Robust Exponential Converge Controller Design for a Unified Chaotic System with Structured Uncertainties via LMI." Discrete Dynamics in Nature and Society 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/948590.

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This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the linear matrix inequality (LMI) form. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to enforce the prespecified exponential decay dynamics of the uncertain unified chaotic system. Numerical results validate the effectiveness of the proposed robust control scheme.

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5

Deb Majumder, Samarpan. "Flight optimisation of missile using linear matrix inequality (LMI) approach." Journal of Engineering 2020, no. 7 (2020): 247–50. http://dx.doi.org/10.1049/joe.2019.0952.

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6

Krokavec, Dušan, and Anna Filasová. "LMI Based Principles in Strictly Metzlerian Systems Control Design." Mathematical Problems in Engineering 2018 (July 17, 2018): 1–14. http://dx.doi.org/10.1155/2018/9590253.

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The paper is concerned with the design requirements that relax the existing conditions reported in the previous literature for continuous-time linear positive systems, reformulating the linear programming approach by the linear matrix inequalities principle. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteeing asymptotic stability of positive system structures, the conditions are presented, with which the state-feedback controllers and the system state observers can be designed. A numerical example illustrates the proposed conditions.

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7

Zhao, De Gong, and Yue Chao Ma. "Robust Fault-Tolerant Control for a Class of Uncertain Discrete Time-Delay Systems." Advanced Materials Research 532-533 (June 2012): 521–26. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.521.

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The problem of robust fault-tolerant control for the uncertain time-delay system with state and control delays is studied.The considered system has sensor or actuator failures.Based on Lyapunov stability theory and linear matrix inequality(LMI),a method of robust fault-tolerant against sensor or actuator failures for uncertain system was proposed via memoryless feedback control law.The sufficient for the closed-loop system possessing integrity against sensor or actuator failures are given.At the same time,the controller design method is the linear matrix inequality(LMI).Finally,the numerical example and simulations demonstrate the validity of the proposed method.

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8

Ren, Zerong, and Jun-kang Tian. "Stability Analysis of Systems with Interval Time-Varying Delays via a New Integral Inequality." Complexity 2020 (February 21, 2020): 1–7. http://dx.doi.org/10.1155/2020/2854293.

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This paper focuses on delay-dependent stability analysis for systems with interval time-varying delays. Based on a new integral inequality and a generalized reciprocally convex combination matrix inequality, a new delay-dependent stability criterion is obtained in terms of a linear matrix inequality (LMI). Finally, the merits of the proposed criterion are shown by two numerical examples.

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9

Shi, Shuhui, Guoliang Wang, Jianhua Wang, and Hong Li. "Passive Control of Switched Singular Systems via Output Feedback." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/573950.

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An instrumental matrix approach to design output feedback passive controller for switched singular systems is proposed in this paper. The nonlinear inequality condition including Lyapunov inverse matrix and controller gain matrix is decoupled by introducing additional instrumental matrix variable. Combined with multiple Lyapunov function method, the nonlinear inequality is transformed into linear matrix inequality (LMI). An LMI condition is presented for switched singular system to be stable and passive via static output feedback under designed switching signal. Moreover, the conditions proposed do not require the decomposition of Lyapunov matrix and its inverse matrix or fixing to a special structure. The theoretical results are verified by means of an example. The method introduced in the paper can be effectively extended to a single singular system and normal switched system.

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10

Shi, Hai Bin, and Li Qi. "Regional Pole Placement via Static Output Feedback Based on Coordinate Transformation." Advanced Materials Research 546-547 (July 2012): 916–21. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.916.

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This paper focuses on the regional pole placement via static output feedback. Under proper state coordinate transformation with a free matrix variable, the static output feedback gain may be obtained by solving a linear matrix inequality (LMI). The LMI is feasible only if the poles of a dummy control system are in the given LMI region. The free matrix variable can regulate the dummy system as a state feedback gain matrix. So once the free variable is determined, the static output feedback gain matrix may be obtained by an LMI-based method. The main computations do not concern any reduction or enlargement of matrix inequalities. Numerical examples show the effectiveness of the proposed algorithm.

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11

Huo, Yuhong, and Jia-Bao Liu. "Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems." Mathematics 7, no. 3 (2019): 217. http://dx.doi.org/10.3390/math7030217.

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The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.

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12

Mao, Bei Xing, and Dong Xiao Wang. "Stability Analysis of a Class of Switched Lurie Systems." Advanced Materials Research 171-172 (December 2010): 584–87. http://dx.doi.org/10.4028/www.scientific.net/amr.171-172.584.

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Stability problem of a class of Lurie switched systems is investigated. All the subsystems of a class of switched systems are Lurie systems .The switching law is given using linear matrix inequality(LMI) and Lyapunov functions . The conclusion is given in LMI, so it is easy to realize.

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13

Filasová, Anna, Daniel Gontkovič, and Dušan Krokavec. "LMI based control design for linear systems with distributed time delays." Archives of Control Sciences 22, no. 2 (2012): 217–31. http://dx.doi.org/10.2478/v10170-011-0021-3.

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LMI based control design for linear systems with distributed time delaysThe paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.

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14

Wang, H., J. Lam, S. X. Ding, and M. Zhong. "Iterative linear matrix inequality algorithms for fault detection with unknown inputs." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 219, no. 2 (2005): 161–72. http://dx.doi.org/10.1243/095965105x9489.

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This paper deals with the fault detection problem for linear time-invariant systems with unknown disturbances. Two separate performance indices are presented to facilitate the design of desirable fault detection observers. Iterative linear matrix inequality (LMI) algorithms are proposed in order to design a fault detection observer that aims at enhancing the fault detection and attenuating the effects due to unknown inputs. Numerical examples are employed to demonstrate the effectiveness of the proposed methods.

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15

Ou, Liuli, Shaobo Han, Yongji Wang, Shuai Dong, and Lei Liu. "Partial Pole Placement in LMI Region." Journal of Control Science and Engineering 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/840128.

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A new approach for pole placement of single-input system is proposed in this paper. Noncritical closed loop poles can be placed arbitrarily in a specified convex region when dominant poles are fixed in anticipant locations. The convex region is expressed in the form of linear matrix inequality (LMI), with which the partial pole placement problem can be solved via convex optimization tools. The validity and applicability of this approach are illustrated by two examples.

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16

Liu, Xiu, Shou Ming Zhong, and Xiu Yong Ding. "Exponential Stability for Uncertain Switched Neutral Systems with Nonlinear Perturbations." Advanced Materials Research 217-218 (March 2011): 668–73. http://dx.doi.org/10.4028/www.scientific.net/amr.217-218.668.

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The global exponential stability for switched neutral systems with time-varying delays and nonlinear perturbations is investigated in this paper. LMI-based delay-dependent criterion is proposed to guarantee exponential stability for our considered systems under any switched signal. Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results. Free weighting matrix and linear matrix inequality (LMI) approaches are used to solve the proposed conditions.

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17

Rao, Ruofeng, and Zhilin Pu. "LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/261353.

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By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.

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18

Song, Qiankun, and Jinde Cao. "Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays." Discrete Dynamics in Nature and Society 2010 (2010): 1–19. http://dx.doi.org/10.1155/2010/810408.

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The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

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19

BOCHNIAK, JACEK, and KRZYSZTOF GALKOWSKI. "LMI-BASED ANALYSIS FOR CONTINUOUS-DISCRETE LINEAR SHIFT-INVARIANT nD SYSTEMS." Journal of Circuits, Systems and Computers 14, no. 02 (2005): 307–32. http://dx.doi.org/10.1142/s0218126605002350.

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In this paper, we describe the Linear Matrix Inequality (LMI) approach to the analysis and the synthesis of continuous-discrete linear shift-invariant multidimensional systems presented in the Roesser form. We consider stability, stability margins, robust stability, stabilization and stabilization to the prescribed stability margins and robust stabilization. An example is included as illustrations of the obtained results.

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20

Hammachukiattikul, Porpattama. "Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays." Emerging Science Journal 3, no. 6 (2019): 361–68. http://dx.doi.org/10.28991/esj-2019-01198.

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The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).

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21

Yuan, Zhi, Li Na Wu, Zheng Fang Wang, and Jie Liu. "Robust Fault Estimation Based on Adaptive Observer." Advanced Materials Research 791-793 (September 2013): 888–91. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.888.

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This paper investigates the adaptive observer-based robust fault estimation problem for linear uncertain systems with disturbances. Sufficient conditions for the existence of such a fault estimation observer are given in terms of matrix inequalities. The solution is obtained by the linear matrix inequality (LMI) technique. An example is given to demonstrate the effectiveness of the proposed approach.

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Kim, EuiYong, Waon-Ho Yi, and Jae-Seung Hwang. "Optimal Design of Vibration Control System for a Structure Based on Linear Matrix Inequality Approach." Journal of the Wind Engineering Institute of Korea 23, no. 4 (2019): 203–9. http://dx.doi.org/10.37109/weik.2019.23.4.203.

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23

Leite, Valter J. S., and Márcio F. Miranda. "Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach." Mathematical Problems in Engineering 2008 (2008): 1–15. http://dx.doi.org/10.1155/2008/875609.

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Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

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Habibi, Reza. "Arbitrage Detection Using AHP and LMI Algorithms." Management and Economics Research Journal 04 (2018): 140. http://dx.doi.org/10.18639/merj.2018.04.653192.

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In this paper, the arbitrage opportunities in a foreign exchange market are detected using analytic hierarchy process and linear matrix inequality methods. For this purpose, first, criteria are proposed to detect the direct, triangular, quadrangular, and other types of arbitrage suspect existing in a foreign exchange market. Subsequently, the optimal arbitrage paths are given. Some simulated examples are given. A real data set is analyzed as well. Finally, a conclusion section is given.

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Chen, Xiaofeng, Qiankun Song, Xiaohui Liu та Zhenjiang Zhao. "Globalμ-Stability of Complex-Valued Neural Networks with Unbounded Time-Varying Delays". Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/263847.

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The complex-valued neural networks with unbounded time-varying delays are considered. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the globalμ-stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

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KUNTANAPREEDA, SUWAT. "SIMPLE LMI-BASED SYNCHRONIZATION OF FRACTIONAL-ORDER CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 23, no. 01 (2013): 1350011. http://dx.doi.org/10.1142/s0218127413500119.

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This paper presents a simple scheme for synchronization of fractional-order chaotic systems. The scheme utilizes a recently developed LMI (Linear matrix inequality) stabilization theorem for fractional-order linear interval systems to design a linear controller. In contrast to existing schemes in the literature, the present scheme is straightforward and does not require that nonlinear parts of synchronization error dynamics are cancelled by the controller. The fractional-order Rössler, Lorenz, and hyperchaotic Chen systems are used as demonstrative examples. Numerical results illustrate the effectiveness of the present scheme.

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Gong, Dawei, Frank L. Lewis, Liping Wang, Dong Dai, and Shuang Zhang. "Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma." Complexity 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/2137103.

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The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.

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Cong, Xin-rong, and Long-suo Li. "Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach." Journal of Function Spaces and Applications 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/873578.

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This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

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CHEN, CHEN-YUAN, JOHN RONG-CHUNG HSU, and CHENG-WU CHEN. "FUZZY LOGIC DERIVATION OF NEURAL NETWORK MODELS WITH TIME DELAYS IN SUBSYSTEMS." International Journal on Artificial Intelligence Tools 14, no. 06 (2005): 967–74. http://dx.doi.org/10.1142/s021821300500248x.

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This paper extends the Takagi-Sugeno (T-S) fuzzy model representation to analyze the stability of interconnected systems in which there exist time delays in subsystems. A novel stability criterion which can be solved numerically is presented in terms of Lyapunov's theory for fuzzy interconnected models. In this paper, we use linear difference inclusion (LDI) state-space representation to represent the fuzzy model. Then, the linear matrix inequality (LMI) optimization algorithm is employed to find common solution and then guarantee the asymptotic stability.

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WEN, GUILIN, QING-GUO WANG, CHONG LIN, GUANGYAO LI, and XU HAN. "CHAOS SYNCHRONIZATION VIA MULTIVARIABLE PID CONTROL." International Journal of Bifurcation and Chaos 17, no. 05 (2007): 1753–58. http://dx.doi.org/10.1142/s0218127407018051.

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Synchronization via multivariable PID control is studied. Based on the descriptor approach, the problem of PID controller design is transformed to that of static output feedback (SOF) controller design. The improvement of the solvability of the Linear Matrix Inequality (LMI) is achieved, in comparison with the existing literature on designing PID controller based on the LMI technique. With the aid of the free-weighting matrix approach and the S-procedure, the synchronization criterion for a general Lur'e system is established based on the LMI technique. The feasibility of the methodology is illustrated by the well-known Chua's circuit.

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31

Yao, Deyin, Hamid Reza Karimi, Yiyong Sun, and Qing Lu. "Robust Model Predictive Control of Networked Control Systems under Input Constraints and Packet Dropouts." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/478567.

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This paper deals with the problem of robust model predictive control (RMPC) for a class of linear time-varying systems with constraints and data losses. We take the polytopic uncertainties into account to describe the uncertain systems. First, we design a robust state observer by using the linear matrix inequality (LMI) constraints so that the original system state can be tracked. Second, the MPC gain is calculated by minimizing the upper bound of infinite horizon robust performance objective in terms of linear matrix inequality conditions. The method of robust MPC and state observer design is illustrated by a numerical example.

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Kokil, Priyanka. "An LMI Based Criterion for Global Asymptotic Stability of Discrete-Time State-Delayed Systems with Saturation Nonlinearities." International Scholarly Research Notices 2014 (October 29, 2014): 1–6. http://dx.doi.org/10.1155/2014/761959.

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A linear matrix inequality (LMI) based criterion for the global asymptotic stability of discrete-time systems with multiple state-delays employing saturation nonlinearities is presented. Numerical examples highlighting the effectiveness of the proposed criterion are given.

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Ni, Huai Sheng, Feng Xiang Chen, and Tong Zhang. "Robust Observer for a Class of Linear System with Matched Uncertainty Based on LMI." Advanced Materials Research 791-793 (September 2013): 1427–30. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.1427.

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In this paper, a novel framework of robust observer for linear system with parametric uncertain state matrix matched with output matrix is introduced. The scheme is derived by including an extra term to the feedback gain, and the term is obtained by the analysis of the Lyapunov stability theory and LMI (Linear Matrix Inequality). The proposed observer is less conservative and thus lead to a low gain matrix based on the novel framework. Finally, the effectiveness of the proposed method is validated by the numerical simulations on Matlab environment.

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Wo, Song Lin, and Xiao Xin Han. "Finite-Time Stability for Continuous-Time Linear Singular Systems." Advanced Materials Research 846-847 (November 2013): 383–87. http://dx.doi.org/10.4028/www.scientific.net/amr.846-847.383.

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In this paper the finite-time stability (FST) problem of continuous-time linear singular systems (CTLSS) is considered. The main results provided are a sufficient condition of FTS for CTLSS and a sufficient condition of robust FTS for uncertain CTLSS. Such sufficient conditions in the LMI formalism are attained for finite-time stability; this gives the opportunity of fitting the finite time stability problem in the general framework of the linear matrix inequality (LMI) approach. In this context an example is provided to demonstrate the application of the proposed method for CTLSS finite-time stability problem.

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Abdalla, Musa, and Tamir Shagarin. "Industrial Process Control Using LPV." Modern Applied Science 11, no. 9 (2017): 39. http://dx.doi.org/10.5539/mas.v11n9p39.

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An industrial process control application of level and temperature is considered. The nonlinear mathematical model of the system is cast as a linear parameter varying (LPV) system. A linear matrix inequality (LMI) type of controller is successfully designed using the LMI unified approach to regulating both controlled variables, namely; temperature and level. The closed loop system is then implemented through computer simulation to show the effectiveness of the controller in performing the combined level-temperature regulation. Basically, this combined level and temperature industrial control application is used to demonstrate the effectiveness of post-modern controllers; in this case LMI based controllers.

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Li, Sha-sha, Zhan-shan Zhao, Jing Zhang, Jie Sun, and Lian-kun Sun. "H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/4908459.

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The issue of H∞ control for the coronary artery input time-delay system with external disturbance is of concern. To further reduce conservation, we utilize the free-matrix-based integral inequality, Wirtinger-based integral inequality, and reciprocal convex combination approach to construct Lyapunov-Krasovskii function (LKF). Then a sufficient condition for controller design which can guarantee robust synchronization the coronary artery system is represented in terms of linear matrix inequality (LMI). Finally, a numerical example is exploited to show the effectiveness of the proposed methods.

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Dabboussi, Kamel, and Jalel Zrida. "Sufficient Dilated LMI Conditions for Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/812920.

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New sufficient dilated linear matrix inequality (LMI) conditions for the static output feedback control problem of linear continuous-time systems with no uncertainty are proposed. The used technique easily and successfully extends to systems with polytopic uncertainties, by means of parameter-dependent Lyapunov functions (PDLFs). In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with even more relaxed structure are employed. It is shown that these slack variables provide additional flexibility to the solution. It is also shown, in this paper, that the proposed dilated LMI-based conditions always encompass the standard LMI-based ones. Numerical examples are given to illustrate the merits of the proposed method.

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Boukas and, E. K., and Z. K. Liu. "Robust Stability and H∞ Control of Discrete-Time Jump Linear Systems With Time-Delay: An LMI Approach*." Journal of Dynamic Systems, Measurement, and Control 125, no. 2 (2003): 271–77. http://dx.doi.org/10.1115/1.1570858.

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This paper considers the class of discrete-time jump linear systems with time-delay and polytopic uncertain parameters. The problems of delay-independent robust stability, stabilization and H∞ control are cast into the framework of linear matrix inequality (LMI) and thus solved by LMI Toolbox of Matlab. By extending the system state, the system with time-delay is converted into a higher dimension Markov jump system without time-delay, and thus can be handled as a standard jump linear system with uncertain parameters. Numerical examples are provided to show the usefulness of the theoretical results.

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Jin, Jie. "Robust Absolute Stabilization of Time-Varying Delay Systems with Maximum Admissible Perturbed Bound." Applied Mechanics and Materials 40-41 (November 2010): 103–10. http://dx.doi.org/10.4028/www.scientific.net/amm.40-41.103.

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This paper is concerned the problem of robust absolute stabilization of time-varying delay systems with admissible perturbation in terms of integral inequality. A linear state-feedback control law is derived for one class of delay systems with sector restriction based on linear matrix inequality (LMI). Especially, this method does not require input terms are absolutely controllable for nonlinear delay systems. Numerical example is used to demonstrate the validity of the proposed method.

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40

Soliman, Hisham M., and Mahmoud Soliman. "Design of Observer-Based Robust Power System Stabilizers." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 5 (2016): 1956. http://dx.doi.org/10.11591/ijece.v6i5.11802.

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<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. The present manuscript proposes two designs for observer-based robust power system stabilizer (PSS) using Linear Matrix Inequality (LMI) approach to damp such oscillations. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite settling time and damping ratio via a non-iterative solution to a set of LMIs. The approach provides a systematic way to design a robust output feedback PSS which guarantees good dynamic performance for different loads. <span style="font-size: 10px;">Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</span></p>

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41

Soliman, Hisham M., and Mahmoud Soliman. "Design of Observer-Based Robust Power System Stabilizers." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 5 (2016): 1956. http://dx.doi.org/10.11591/ijece.v6i5.pp1956-1966.

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<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. The present manuscript proposes two designs for observer-based robust power system stabilizer (PSS) using Linear Matrix Inequality (LMI) approach to damp such oscillations. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite settling time and damping ratio via a non-iterative solution to a set of LMIs. The approach provides a systematic way to design a robust output feedback PSS which guarantees good dynamic performance for different loads. <span style="font-size: 10px;">Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</span></p>

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42

Iwasaki, T., and R. E. Skelton. "A unified approach to fixed-order controller design via linear matrix inequalities." Mathematical Problems in Engineering 1, no. 1 (1995): 59–75. http://dx.doi.org/10.1155/s1024123x9500007x.

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We consider the design of fixed-order (or low-order) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,𝒬-stabilization as a robust stabilization problem, and robustL∞control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI) of the typeBGC+(BGC)T+Q<0for the unknown matrixG. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured) positive definite matrixXsuch thatX∈𝒞1andX−1∈𝒞2where𝒞1and𝒞2are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

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Xiao, Li, Xiaofeng Liao, and Huiwei Wang. "Cluster Consensus on Discrete-Time Multi-Agent Networks." Abstract and Applied Analysis 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/274735.

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Nowadays, multi-agent networks are ubiquitous in the real world. Over the last decade, consensus has received an increasing attention from various disciplines. This paper investigates cluster consensus for discrete-time multi-agent networks. By utilizing a special coupling matrix and the Kronecker product, a criterion based on linear matrix inequality (LMI) is obtained. It is shown that the addressed discrete-time multi-agent networks achieve cluster consensus if a certain LMI is feasible. Finally, an example is given to demonstrate the effectiveness of the proposed criterion.

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Zhang, Weiwei, and Linshan Wang. "Robust Stochastic Stability Analysis for Uncertain Neutral-Type Delayed Neural Networks Driven by Wiener Process." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/829594.

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The robust stochastic stability for a class of uncertain neutral-type delayed neural networks driven by Wiener process is investigated. By utilizing the Lyapunov-Krasovskii functional and inequality technique, some sufficient criteria are presented in terms of linear matrix inequality (LMI) to ensure the stability of the system. A numerical example is given to illustrate the applicability of the result.

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Liu, Guoquan, Shumin Zhou, and He Huang. "New LMI-Based Conditions on Neural Networks of Neutral Type with Discrete Interval Delays and General Activation Functions." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/306583.

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The stability analysis of global asymptotic stability of neural networks of neutral type with both discrete interval delays and general activation functions is discussed. New delay-dependent conditions are obtained by using more general Lyapunov-Krasovskii functionals. Meanwhile, these conditions are expressed in terms of a linear matrix inequality (LMI) and can be verified using the MATLAB LMI toolbox. Numerical examples are used to illustrate the effectiveness of the proposed approach.

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Wang, Hua, Xian-Hai Shen, Liang-Xu Zhang, and Xiao-Jin Zhu. "Active vibration suppression of flexible structure using a LMI-based control patch." Journal of Vibration and Control 18, no. 9 (2011): 1375–79. http://dx.doi.org/10.1177/1077546311415303.

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Based on the linear matrix inequality, a linear feedback control is presented to realize active vibration suppression of a class of flexible structure. By introducing an appropriate modal transformation, the controller design procedure can be simplified greatly. A specific Lyapunov function is adopted to induce the asymptotical stability of the flexible structure. Simulation results for flexible spacecraft are provided to illustrate the effectiveness of the proposed scheme.

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Xing, Hai Long, and Wen Shan Cui. "Feedback Control of Parabolic Distributed Parameter Systems." Applied Mechanics and Materials 455 (November 2013): 337–43. http://dx.doi.org/10.4028/www.scientific.net/amm.455.337.

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In this paper, the feedback control problem is considered for a class of parabolic distributed parameter systems (DPS). By employing a new Lyapunov-Krasovskii functional as well as the linear matrix inequality (LMI), a novel feedback controller is developed, which can guarantee the closed-loop system states uniformly convergent to zero. The stability conditions for closed-loop systems can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. At last, a numerical example shows the effectiveness of the presented LMI-based methods.

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Qin, Lu Fang, Tao Sun, and Hua Feng Guo. "Robust Control of Variable Pitch Wind Turbines Base on Linear Matrix Inequality." Advanced Materials Research 291-294 (July 2011): 2754–59. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.2754.

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In order to solve the problems of wind power generation system model uncertainty, we designed a robust tracking controller according to the robust control theories and the method of linear matrix inequality (LMI). For ensuring the stability and dynamic characteristics of robust, we gave the calculating method of proportion and integral gains, researched the robust control strategy with pole constraint that is based on minimal power tracking controller. The results of the simulation show the controller can realize the steady close-loop and possess good disturbance rejection and dynamic characteristic in some disturbances and uncertainties existed in system.

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JEYAKUMAR, VAITHILINGAM, and ZHIYOU WU. "CONDITIONS FOR GLOBAL OPTIMALITY OF QUADRATIC MINIMIZATION PROBLEMS WITH LMI CONSTRAINTS." Asia-Pacific Journal of Operational Research 24, no. 02 (2007): 149–60. http://dx.doi.org/10.1142/s021759590700119x.

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In this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) constraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints.

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Wang, Yi Zhong. "Proportional-Integral Control for Markovian Jumping Systems with Distributed Time Delay." Advanced Materials Research 562-564 (August 2012): 1689–92. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1689.

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This paper deals with the proportional-integral control problem for a class of stochastic Markovian jum v-Krasovskii functional and free-weighting matrix method, the novel delay-dependent robust stabilization criterion for the stochastic Markovian jumping systems is formulated in terms of linear matrix inequality (LMI). When the LMI is feasible, an explicit expression of the desired proportional-integral controller is given. Designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system for all admissible uncertainties and time delay.

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