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Journal articles on the topic 'Lyapunov-based approach'

Author: Grafiati

Published: 15 June 2024

Last updated: 31 July 2025

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1

Hoang, H., F. Couenne, C. Jallut, and Y. Le Gorrec. "Thermodynamic approach for Lyapunov based control." IFAC Proceedings Volumes 42, no. 11 (2009): 357–62. http://dx.doi.org/10.3182/20090712-4-tr-2008.00056.

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2

Dixon, W. E., E. Zergeroglu, D. M. Dawson, and B. T. Costic. "Repetitive learning control: a Lyapunov-based approach." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 32, no. 4 (2002): 538–45. http://dx.doi.org/10.1109/tsmcb.2002.1018772.

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3

Kansha, Yasuki, Li Jia, and Min-Sen Chiu. "Self-tuning PID controllers based on the Lyapunov approach." Chemical Engineering Science 63, no. 10 (2008): 2732–40. http://dx.doi.org/10.1016/j.ces.2008.02.026.

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4

Abdelmalek, Ibtissem, Noureddine Goléa, and Mohamed Hadjili. "A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models." International Journal of Applied Mathematics and Computer Science 17, no. 1 (2007): 39–51. http://dx.doi.org/10.2478/v10006-007-0005-4.

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A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy ModelsIn this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The prop

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5

Senthilkumar, L., M. Meenakshi, and J. Vasantha Kumar. "Lyapunov Optimization Based Cross Layer Approach for Green Cellular Network." Journal of Green Engineering 5, no. 2 (2016): 129–50. http://dx.doi.org/10.13052/jge1904-4720.523.

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6

Margaliot, Michael, and Gideon Langholz. "Fuzzy Lyapunov-based approach to the design of fuzzy controllers." Fuzzy Sets and Systems 106, no. 1 (1999): 49–59. http://dx.doi.org/10.1016/s0165-0114(98)00356-x.

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7

Hoang, N. Ha, Denis Dochain, and Nicolas Hudon. "A thermodynamic approach towards Lyapunov based control of reaction rate." IFAC Proceedings Volumes 47, no. 3 (2014): 9117–22. http://dx.doi.org/10.3182/20140824-6-za-1003.01958.

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8

Mutlu, Ilhan, Frank Schrödel, Naim Bajcinca, Dirk Abel, and M. Turan Söylemez. "Lyapunov Equation Based Stability Mapping Approach: A MIMO Case Study." IFAC-PapersOnLine 49, no. 9 (2016): 130–35. http://dx.doi.org/10.1016/j.ifacol.2016.07.512.

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9

Masoumnezhad, Mojtaba, Maziar Rajabi, Amirahmad Chapnevis, et al. "An Approach for the Global Stability of Mathematical Model of an Infectious Disease." Symmetry 12, no. 11 (2020): 1778. http://dx.doi.org/10.3390/sym12111778.

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The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The r

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10

Kuzmych, Olena, Abdel Aitouche, Ahmed El Hajjaji, and Jerome Bosche. "Nonlinear control for a diesel engine: A CLF-based approach." International Journal of Applied Mathematics and Computer Science 24, no. 4 (2014): 821–35. http://dx.doi.org/10.2478/amcs-2014-0061.

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Abstract In this paper, we propose a control Lyapunov function based on a nonlinear controller for a turbocharged diesel engine. A model-based approach is used which predicts the experimentally observed engine performance for a biodiesel. The basic idea is to develop an inverse optimal control and to employ a Lyapunov function in order to achieve good performances. The obtained controller gain guarantees the global convergence of the system and regulates the flows for the variable geometry turbocharger as well as exhaust gas recirculation systems in order to minimize the NOx emission and the s

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11

Azhmyakov, Vadim. "Stability of differential inclusions: A computational approach." Mathematical Problems in Engineering 2006 (2006): 1–15. http://dx.doi.org/10.1155/mpe/2006/17837.

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We present a technique for analysis of asymptotic stability for a class of differential inclusions. This technique is based on the Lyapunov-type theorems. The construction of the Lyapunov functions for differential inclusions is reduced to an auxiliary problem of mathematical programming, namely, to the problem of searching saddle points of a suitable function. The computational approach to the auxiliary problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems described by difference inclusions. The obtained numerical schemes are applied

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12

Silva, Cristina, Tonametl Sanchez, David A. Lizárraga Navarro, and Arturo Zavala-Río. "Study of a Lyapunov-based discretization method using the midpoint approach." Memorias del Congreso Nacional de Control Automático 7, no. 1 (2024): 7–12. https://doi.org/10.58571/cnca.amca.2024.002.

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We propose a modification of an existing discretization technique. The technique we atempt to improve is a discretization method designed for homogeneous systems, characterized by first-order consistency, numerical convergence, and the noteworthy feature of preserving both the stability of the system’s equilibrium point and the type of convergence of the solutions toward the origin. Its design is based on the projection of the dynamics of the system over a level surface of the Lyapunov function, and the complementary use of the explicit Euler method. In this work the Euler’s explicit method is

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13

Benaoumeur, Ibari, Benchikh Laredj, Haniﬁ Elhachimi Amar Reda, and Ahmed-foitih Zoubir. "Backstepping Approach for Autonomous Mobile Robot Trajectory Tracking." Indonesian Journal of Electrical Engineering and Computer Science 2, no. 3 (2016): 478. http://dx.doi.org/10.11591/ijeecs.v2.i3.pp478-485.

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This paper proposes a backstepping controller design for trajectory tracking of unicycle-type mobile robots. The main object of the control algorithms developed is to design a robust output tracking controller. The design of the controller is based on the lyapunov theorem, kinematic tracking controller of an unicycle-like mobile robot is used to provides the desired values of the linear and angular velocities for the given trajectory. A Lyapunov-based stability analysis is presented to guarantee the robot stability of the tracking errors. Simulation and experimental results show the effectiven

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14

Zhao, Yongchi, Shengxian Zhuang, Weiming Xiang, and Lin Du. "Discretized Lyapunov Function Approach for Switched Linear Systems under Dwell Time Constraint." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/905968.

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This paper is concerned with the stability and disturbance attenuation properties of switched linear system with dwell time constraint. A novel time-scheduled Lyapunov function is introduced to deal with the problems studied in this paper. To numerically check the existence of such time-scheduled Lyapunov function, the discretized Lyapunov function technique usually used in time-delay system is developed in the context of switched system in continuous-time cases. Based on discretized Lyapunov function, sufficient conditions ensuring dwell-time constrained switched system global uniformly asymp

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15

SHEN, Tielong, and Katsutoshi TAMURA. "Nonlinear Robust H^|^infin; Control-An Approach Based on Lyapunov Function-." Transactions of the Society of Instrument and Control Engineers 34, no. 9 (1998): 1191–97. http://dx.doi.org/10.9746/sicetr1965.34.1191.

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16

Hong, Yiguang, Lixin Gao, Daizhan Cheng, and Jiangping Hu. "Lyapunov-Based Approach to Multiagent Systems With Switching Jointly Connected Interconnection." IEEE Transactions on Automatic Control 52, no. 5 (2007): 943–48. http://dx.doi.org/10.1109/tac.2007.895860.

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17

Xu, Xiang, Lu Liu, and Gang Feng. "Stability and Stabilization of Infinite Delay Systems: A Lyapunov-Based Approach." IEEE Transactions on Automatic Control 65, no. 11 (2020): 4509–24. http://dx.doi.org/10.1109/tac.2019.2958557.

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18

Xu, Jun, Daoying Pi, Yong-Yan Cao, and Shouming Zhong. "On Stability of Neural Networks by a Lyapunov Functional-Based Approach." IEEE Transactions on Circuits and Systems I: Regular Papers 54, no. 4 (2007): 912–24. http://dx.doi.org/10.1109/tcsi.2007.890604.

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19

Arjmandzadeh, Ziba, Mohammad Hossein Abbasi, Hanchen Wang, Jiangfeng Zhang, and Bin Xu. "A Lyapunov Optimization-Based Approach to Autonomous Vehicle Local Path Planning." Sensors 24, no. 24 (2024): 8031. https://doi.org/10.3390/s24248031.

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Autonomous vehicles (AVs) offer significant potential to improve safety, reduce emissions, and increase comfort, drawing substantial attention from both research and industry. A critical challenge in achieving SAE Level 5 autonomy, full automation, is path planning. Ongoing efforts in academia and industry are focused on optimizing AV path planning, reducing computational complexity, and enhancing safety. This paper presents a novel approach using Lyapunov Optimization (LO) for local path planning in AVs. The proposed LO model is benchmarked against two conventional methods: model predictive c

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20

Fridman, Emilia. "Stability of linear descriptor systems with delay: a Lyapunov-based approach." Journal of Mathematical Analysis and Applications 273, no. 1 (2002): 24–44. http://dx.doi.org/10.1016/s0022-247x(02)00202-0.

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21

Hoang, Nguyen Quang, and Soon Geul Lee. "Energy-Based Approach for Controller Design of Overhead Cranes: A Comparative Study." Applied Mechanics and Materials 365-366 (August 2013): 784–87. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.784.

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In this paper, five controllers including linear and nonlinear ones for an underactuated overhead crane are derived based on the passivity of the system. The total energy of the system and its square are used in Lyapunov candidate function to design controllers. The equilibrium point of the closed loop is proven to be asymptotically stable by the Lyapunov technique and LaSalle invariance theorem. In addition, the optimal linear controller is also combined to force the swing angle to converge fast to zero by reaching destination of the trolley. Numerical simulations are carried out to evaluate

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22

Martin, Christoph, Nahal Sharafi, and Sarah Hallerberg. "Estimating covariant Lyapunov vectors from data." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 3 (2022): 033105. http://dx.doi.org/10.1063/5.0078112.

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Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications, it is necessary to estimate these vectors from data since model equations are unknown for many interesting phenomena. We propose an approach for estimating covariant Lyapunov vectors based on data records without knowing the underlying equations of the system. In contrast to previous approaches, our approach can be applied to high-dimensional datasets. We demonstrate that this pur

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23

HAN, R., M. LEMM, and W. SCHLAG. "Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base." Ergodic Theory and Dynamical Systems 40, no. 10 (2019): 2788–853. http://dx.doi.org/10.1017/etds.2019.19.

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We prove a conditional theorem on the positivity of the Lyapunov exponent for a Schrödinger cocycle over a skew-shift base with a cosine potential and the golden ratio as frequency. For coupling below 1, which is the threshold for Herman’s subharmonicity trick, we formulate three conditions on the Lyapunov exponent in a finite but large volume and on the associated large-deviation estimates at that scale. Our main results demonstrate that these finite-size conditions imply the positivity of the infinite-volume Lyapunov exponent. This paper shows that it is possible to make the techniques devel

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24

Ates, Muzaffer, and Nezir Kadah. "Novel stability and passivity analysis for three types of nonlinear LRC circuits." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 11, no. 2 (2021): 227–37. http://dx.doi.org/10.11121/ijocta.01.2021.001073.

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In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapun

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25

Vafamand, Navid. "Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach." Journal of Vibration and Control 26, no. 19-20 (2020): 1765–78. http://dx.doi.org/10.1177/1077546320904817.

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This article studies the problem of global stability of the Takagi–Sugeno fuzzy systems based on a novel descriptor-based non-quadratic Lyapunov function. A modified non-quadratic Lyapunov function, which comprises an integral term of the membership functions, and a modified non-parallel distributed controller constructed by constant delayed premise variables are considered that assure the global stability of the closed-loop T–S fuzzy system. The special structure of the used non-quadratic Lyapunov function results in time-delayed terms of the membership functions, instead of appearing their t

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26

Мamyrbek, Beisenbi, and Kaliyeva Samal. "Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions." Eastern-European Journal of Enterprise Technologies 1, no. 3 (121) (2023): 6–14. https://doi.org/10.15587/1729-4061.2023.274063.

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One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions

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27

Namachchivaya, N. Sri, and H. J. Van Roessel. "Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach." Journal of Applied Mechanics 71, no. 6 (2004): 759–68. http://dx.doi.org/10.1115/1.1795813.

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A perturbation approach is used to obtain an approximation for the moment Lyapunov exponent of two coupled oscillators with commensurable frequencies driven by a small intensity real noise with dissipation. The generator for the eigenvalue problem associated with the moment Lyapunov exponent is derived without any restriction on the size of pth moment. An orthogonal expansion for the eigenvalue problem based on the Galerkin method is used to derive the stability results in terms of spectral densities. These results can be applied to study the moment and almost-sure stability of structural and

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28

Zhu, Hailing, Khmaies Ouahada, and Suvendi Rimer. "Real Time Energy Storage Sharing With Load Scheduling: A Lyapunov-Based Approach." IEEE Access 9 (2021): 46626–40. http://dx.doi.org/10.1109/access.2021.3067788.

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29

冷, 轩. "Global Dynamics for a Plant Disease Model Based on Generalized Lyapunov Approach." Advances in Applied Mathematics 10, no. 04 (2021): 1086–95. http://dx.doi.org/10.12677/aam.2021.104117.

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30

Dubljević, Stevan, and Nikolaos Kazantzis. "A new Lyapunov design approach for nonlinear systems based on Zubov's method." Automatica 38, no. 11 (2002): 1999–2007. http://dx.doi.org/10.1016/s0005-1098(02)00110-3.

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31

Wang, Ruigang, and Jie Bao. "A differential Lyapunov-based tube MPC approach for continuous-time nonlinear processes." Journal of Process Control 83 (November 2019): 155–63. http://dx.doi.org/10.1016/j.jprocont.2018.11.006.

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32

Faieghi, Mohammadreza, Seyed Kamal-e.-ddin Mousavi Mashhadi, and Dumitru Baleanu. "Sampled-data nonlinear observer design for chaos synchronization: A Lyapunov-based approach." Communications in Nonlinear Science and Numerical Simulation 19, no. 7 (2014): 2444–53. http://dx.doi.org/10.1016/j.cnsns.2013.11.021.

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33

Wang, Yaonan, Zhiqiang Miao, Hang Zhong, and Qi Pan. "Simultaneous Stabilization and Tracking of Nonholonomic Mobile Robots: A Lyapunov-Based Approach." IEEE Transactions on Control Systems Technology 23, no. 4 (2015): 1440–50. http://dx.doi.org/10.1109/tcst.2014.2375812.

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34

Montoya, Oscar Danilo, and Walter Gil-González. "Nonlinear analysis and control of a reaction wheel pendulum: Lyapunov-based approach." Engineering Science and Technology, an International Journal 23, no. 1 (2020): 21–29. http://dx.doi.org/10.1016/j.jestch.2019.03.004.

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35

TayebiHaghighi, Shahnaz, and Insoo Koo. "Sensor Fault Diagnosis Using a Machine Fuzzy Lyapunov-Based Computed Ratio Algorithm." Sensors 22, no. 8 (2022): 2974. http://dx.doi.org/10.3390/s22082974.

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Anomaly identification for internal combustion engine (ICE) sensors has become an important research area in recent years. In this work, a proposed indirect fuzzy Lyapunov-based computed ratio observer integrated with a support vector machine (SVM) was designed for sensor fault classification. The proposed fuzzy Lyapunov-based computed ratio observer integrated with SVM has three main layers. In the preprocessing (first) layer, the resampled root mean square (RMS) signals are extracted from the original signals to the designed indirect observer. The second (observation) layer is the principal

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36

Aly, Islam A., and Kadriye Merve Dogan. "Discrete-Time Adaptive Control for Uncertain Scalar Multiagent Systems with Coupled Dynamics: A Lyapunov-Based Approach." Electronics 13, no. 3 (2024): 524. http://dx.doi.org/10.3390/electronics13030524.

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Discrete-time architectures offer a distinct advantage over their continuous counterparts, as they can be seamlessly implemented on embedded hardware without the necessity for discretization processes. Yet, because of the difficulty of ensuring Lyapunov difference expressions, their designs, which are based on quadratic Lyapunov-based frameworks, are highly complex. As a result, various existing continuous-time results using adaptive control methods to deal with system uncertainties and coupled dynamics in agents of a multiagent system cannot be directly applied to the discrete-time context. F

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37

Huang, Xi Chang, Zhi Jian Zong, and Zhong Tu Liu. "Robust Nonlinear Control of Electric Power Steering System Based on Lyapunov Redesign." Advanced Materials Research 588-589 (November 2012): 1619–23. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.1619.

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Based on the dynamic characteristics of EPS, whole vehicle and tire, the dynamic equation of the EPS system was established. The Krasovk’s method was used to obtian the candidate Lyapunov function for the EPS system. A nonlinear control for EPS system considering parameter uncertainty was presented by Lyapunov redesign approach. The results were obtained from simulation based on Dymola, where is shown that Control law of EPS have the robust performance.

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38

Liao, Wenqi, Hongbing Zeng, and Huichao Lin. "Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach." Mathematics 12, no. 11 (2024): 1638. http://dx.doi.org/10.3390/math12111638.

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This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints of traditional constant matrix-dependent zero equations. Secondly, for a class of periodic time-varying delays, considering the monotonicity of the delay and combining it with an augmented variable approach, Lyapunov functionals are constructed for monotonically increasing and

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39

Rakhshan, Mohsen, Navid Vafamand, Mohammad Mehdi Mardani, Mohammad-Hassan Khooban, and Tomislav Dragičević. "Polynomial control design for polynomial systems: A non-iterative sum of squares approach." Transactions of the Institute of Measurement and Control 41, no. 7 (2018): 1993–2004. http://dx.doi.org/10.1177/0142331218793476.

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This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and

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40

Uskenbayeva, Gulzhan. "Research of the Robust Stability of Control Systems Using a New Approach to the Lyapunov Functions Construction." Modern Applied Science 9, no. 11 (2015): 176. http://dx.doi.org/10.5539/mas.v9n11p176.

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<p class="22">We investigate a new approach to the construction of vector Lyapunov functions. An approach to the construction of Lyapunov functions as vector functions is developed based on a geometrical interpretation of the second method of Lyapunov. The negative of the gradient is determined from the components of the time derivative of the state vector (i.e., the right-hand side of the state equation). The region of stability of a closed-loop linear, stationary system with uncertain parameters is governed by inequalities in the matrix elements of the closed-loop system. This study de

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41

Beisenbi, Мamyrbek, and Samal Kaliyeva. "Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions." Eastern-European Journal of Enterprise Technologies 1, no. 3 (121) (2023): 6–14. http://dx.doi.org/10.15587/1729-4061.2023.274063.

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One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions

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42

Barreira, Luis, Davor Dragičević, and Claudia Valls. "Tempered exponential dichotomies and Lyapunov exponents for perturbations." Communications in Contemporary Mathematics 18, no. 05 (2016): 1550058. http://dx.doi.org/10.1142/s0219199715500583.

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We establish a Perron-type result for the perturbations of a linear cocycle in the context of ergodic theory. More precisely, we show that the Lyapunov exponents of a linear cocycle are preserved under sufficiently small nonautonomous perturbations. Our approach is based on the Lyapunov theory of regularity.

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43

Hendi, Wicaksono Agung Fransisco Jordan. "Semi-decentralized Lyapunov-based formation control of multiple omnidirectional mobile robots." Indonesian Journal of Electrical Engineering and Computer Science 35, no. 2 (2024): 823–33. https://doi.org/10.11591/ijeecs.v35.i2.pp823-833.

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This paper introduces an advanced formation control algorithm based on a Lyapunov approach for coordinating multiple omnidirectional mobile robots in collaborative object transport tasks. The semi-decentralized strategy ensures that the robots maintain a predefined geometric formation, crucial for stability during material transportation, and dynamically adapt to avoid collisions using onboard sensors. Experimental with a physical robot simulator demonstrates successful maintenance of line and triangle formations achieving an average side length maintenance of 1.00 meters with minimal deviatio

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44

Ante, Jackson E., Michael P. Ineh, Jonas O. Achuobi, Uwem P. Akai, Jeremiah U. Atsu, and Nnanake-Abasi O. Offiong. "A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations." AppliedMath 4, no. 4 (2024): 1600–1617. https://doi.org/10.3390/appliedmath4040085.

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This paper investigates the asymptotic eventual stability (AE-S) for nonlinear impulsive Caputo fractional differential equations (ICFDEs) with fixed impulse moments, employing auxiliary Lyapunov functions (ALF) which are specifically constructed as analogues of vector Lyapunov functions (VLF). A novel derivative tailored for VLF is introduced, offering a more robust framework than existing approaches based on scalar Lyapunov functions (SLF). Adequate conditions for AE-S involving ICFDEs are provided. We also used the predictor corrector method to implement a numerical solution for a given imp

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45

Fiedler, Robert, and Hartmut Hetzler. "Numerical Approximation of LYAPUNOV-Exponents for Quasiperiodic Motions." MATEC Web of Conferences 241 (2018): 01009. http://dx.doi.org/10.1051/matecconf/201824101009.

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This paper proposes an approach to approximate the LYAPUNOV -spectrum of quasiperiodic flows on isolated invariant manifolds numerically. Once the invariant manifold has been determined, integrations over the infinite, one dimensional time interval – as calculating the LYAPUNOV -spectrum for instance – can be transformed into an integral over a finite, p-dimensional domain, where p is the dimension of the manifold. The application of the proposed approach is demonstrated by calculating the LYAPUNOV -spectrum of periodic and quasiperiodic motions of a forced VAN-DER-POL equation. The results ar

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46

Leeghim, Henzeh, Dong-Hyun Cho, Su-Jang Jo, and Donghoon Kim. "Generalized Guidance Scheme for Low-Thrust Orbit Transfer." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/407087.

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The authors present an orbital guidance scheme for the satellite with an electrical propulsion system using a Lyapunov feedback control. The construction of a Lyapunov candidate is based on orbital elements, which consist of angular momentum and eccentricity vectors. This approach performs orbit transfers between any two arbitrary elliptic or circular orbits without any singularity issues. These orbital elements uniquely describe a non degenerate Keplerian orbit. The authors improve the reliability of the existing Lyapunov orbital guidance scheme by considering the energy term. Additional impr

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Arrifano, Natache S. D., Vilma A. Oliveira, and Lúcia V. Cossi. "Synthesis of an LMI-based fuzzy control system with guaranteed cost performance: a piecewise Lyapunov approach." Sba: Controle & Automação Sociedade Brasileira de Automatica 17, no. 2 (2006): 213–25. http://dx.doi.org/10.1590/s0103-17592006000200009.

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A new stability analysis and design of a fuzzy switching control based on uncertain Takagi-Sugeno fuzzy systems are proposed. The fuzzy system adopted is composed by a family of local linear uncertain systems with aggregation. The control design proposed uses local state feedback gains obtained from an optimization problem with guaranteed cost performance formulated in the context of linear matrix inequalities and a fuzzy switching scheme built from local Lyapunov functions. The global stability is guaranteed by considering a class of piecewise quadratic Lyapunov functions. Examples are given

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Zhai, Guisheng, and Xuping Xu. "A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching." International Journal of Applied Mathematics and Computer Science 20, no. 2 (2010): 249–59. http://dx.doi.org/10.2478/v10006-010-0018-2.

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A unified approach to stability analysis of switched linear descriptor systems under arbitrary switchingWe establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the

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Ivanov, Danil, Goncalo Amaro, Yaroslav Mashtakov, Mikhail Ovchinnikov, and Anna Guerman. "Formation Flying Lyapunov-Based Control Using Lorentz Forces." Aerospace 10, no. 1 (2023): 39. http://dx.doi.org/10.3390/aerospace10010039.

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A formation flying control algorithm using the Lorentz force for Low Earth Orbits to achieve a trajectory with required shape and size is proposed in the paper. The Lorentz force is produced as a result of interaction between the Earth’s magnetic field and an electrically charged spacecraft. Achievement of the required trajectories represents a challenge since the control in three-dimensional space is a scalar value of the satellite’s charge. A Lyapunov-based control algorithm is developed for elimination of the initial relative drift after the launch. It also aims at reaching a required ampli

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Wang, Guanping, Wuyin Jin, and An Wang. "The complete synchronization of coupled Morris–Lecar neurons with chemical synapses." International Journal of Modern Physics B 30, no. 17 (2016): 1650096. http://dx.doi.org/10.1142/s021797921650096x.

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Based on the basic principles of stability theory and Lyapunov function, the condition of complete synchronization in coupled Morris–Lecar (ML) neuronal system with chemical synapses is studied in this work. The boundedness of the model solution is proved by analytical approach, the sufficient condition of the complete synchronization is proposed based on the quadratic of the constructed Lyapunov function and the result is verified by simulations.

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