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Journal articles on the topic 'Lyapunov time'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Zagrebina, I. S. "Lyapunov inequality for time scales." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, no. 2 (April 2008): 47–48. http://dx.doi.org/10.20537/vm080216.

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2

Bohner, Martin, Stephen Clark, and Jerry Ridenhour. "Lyapunov inequalities for time scales." Journal of Inequalities and Applications 2002, no. 1 (2002): 829403. http://dx.doi.org/10.1155/s102558340200005x.

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3

Evans, Denis J. "Time correlation relation for Lyapunov exponents." Physical Review Letters 69, no. 3 (July 20, 1992): 395–97. http://dx.doi.org/10.1103/physrevlett.69.395.

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4

Kharitonov, V. L., and E. Plischke. "Lyapunov matrices for time-delay systems." Systems & Control Letters 55, no. 9 (September 2006): 697–706. http://dx.doi.org/10.1016/j.sysconle.2006.01.005.

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5

Tanaka, Toshiyuki, Kazuyuki Aihara, and Masao Taki. "Lyapunov exponents of random time series." Physical Review E 54, no. 2 (August 1, 1996): 2122–24. http://dx.doi.org/10.1103/physreve.54.2122.

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6

Pyragas, K. "Conditional Lyapunov exponents from time series." Physical Review E 56, no. 5 (November 1, 1997): 5183–88. http://dx.doi.org/10.1103/physreve.56.5183.

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7

Bryant, Paul, Reggie Brown, and Henry D. I. Abarbanel. "Lyapunov exponents from observed time series." Physical Review Letters 65, no. 13 (September 24, 1990): 1523–26. http://dx.doi.org/10.1103/physrevlett.65.1523.

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8

Balibrea, Francisco, and María Victoria Caballero. "Using Lyapunov exponents in time series." IEICE Proceeding Series 1 (March 17, 2014): 447–49. http://dx.doi.org/10.15248/proc.1.447.

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9

Li, Huijuan, and Qingxia Ma. "Finite-Time Lyapunov Functions and Impulsive Control Design." Complexity 2020 (October 27, 2020): 1–9. http://dx.doi.org/10.1155/2020/5179752.

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In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

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10

Gao, Wenhua, Feiqi Deng, Ruiqiu Zhang, and Wenhui Liu. "Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/809290.

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This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

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11

RAMARAJAN, S. "Time-varying Lyapunov functions for linear time-varying systems." International Journal of Control 44, no. 6 (December 1986): 1699–702. http://dx.doi.org/10.1080/00207178608933694.

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12

Duda, Józef. "Lyapunov matrices approach to the parametric optimization of time-delay systems." Archives of Control Sciences 25, no. 3 (September 1, 2015): 279–88. http://dx.doi.org/10.1515/acsc-2015-0018.

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AbstractIn the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix

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13

Ding, Zhishuai, Guifang Cheng, and Xiaowu Mu. "W-Stability of Multistable Nonlinear Discrete-Time Systems." Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/418091.

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Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion ofW-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.

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14

Przyborowski, Przemysław, and Tadeusz Kaczorek. "Positive 2D Discrete-Time Linear Lyapunov Systems." International Journal of Applied Mathematics and Computer Science 19, no. 1 (March 1, 2009): 95–106. http://dx.doi.org/10.2478/v10006-009-0009-3.

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Positive 2D Discrete-Time Linear Lyapunov SystemsTwo models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

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15

Fu, Mingyu, Tan Zhang, Fuguang Ding, and Duansong Wang. "Appointed-Time Integral Barrier Lyapunov Function-Based Trajectory Tracking Control for a Hovercraft with Performance Constraints." Applied Sciences 10, no. 20 (October 21, 2020): 7381. http://dx.doi.org/10.3390/app10207381.

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This paper develops a totally new appointed-time integral barrier Lyapunov function-based trajectory tracking algorithm for a hovercraft in the presence of multiple performance constraints and model uncertainties. Firstly, an appointed-time performance constraint function is skillfully designed, which proposes to pre-specify the a priori transient and steady performances on the system tracking errors. Secondly, a new integral barrier Lyapunov function is constructed, which combines with the appointed-time performance constraint function to guarantee that the performance constraints on the system tracking errors are never violated. On this basis, an adaptive trajectory tracking controller is derived using the appointed-time integral barrier Lyapunov function technique in the combination of neural networks. According to Lyapunov’s stability theory, it can be shown that the proposed controller is capable of ensuring transient and steady performances on the output tracking errors. In particular, the position and speed tracking can be fulfilled in a user-appointed time without requiring complex control parameters selection. Finally, results from a comparative simulation study verify the efficacy and advantage of the proposed control approach.

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16

Ding, Ruiqiang, and Jianping Li. "Nonlinear finite-time Lyapunov exponent and predictability." Physics Letters A 364, no. 5 (May 2007): 396–400. http://dx.doi.org/10.1016/j.physleta.2006.11.094.

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17

Zhang, Bin, and Yingmin Jia. "Time-Varying Lyapunov Function for Mechanical Systems." Journal of Robotics, Networking and Artificial Life 5, no. 4 (2019): 241. http://dx.doi.org/10.2991/jrnal.k.190220.007.

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18

Mazenc, F. "Strict Lyapunov functions for time-varying systems." Automatica 39, no. 2 (February 2003): 349–53. http://dx.doi.org/10.1016/s0005-1098(02)00233-9.

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19

Robbé, M., and M. Sadkane. "Discrete-time Lyapunov stability of large matrices." Journal of Computational and Applied Mathematics 115, no. 1-2 (March 2000): 479–94. http://dx.doi.org/10.1016/s0377-0427(99)00185-5.

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20

Prasad, Awadhesh, and Ramakrishna Ramaswamy. "Characteristic distributions of finite-time Lyapunov exponents." Physical Review E 60, no. 3 (September 1, 1999): 2761–66. http://dx.doi.org/10.1103/physreve.60.2761.

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21

Wiesel, William E. "Continuous time algorithm for Lyapunov exponents. I." Physical Review E 47, no. 5 (May 1, 1993): 3686–91. http://dx.doi.org/10.1103/physreve.47.3686.

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22

Wiesel, William E. "Continuous time algorithm for Lyapunov exponents. II." Physical Review E 47, no. 5 (May 1, 1993): 3692–97. http://dx.doi.org/10.1103/physreve.47.3692.

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23

Sadkane, M. "Estimates from the discrete-time Lyapunov equation." Applied Mathematics Letters 16, no. 3 (April 2003): 313–16. http://dx.doi.org/10.1016/s0893-9659(03)80050-2.

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24

Garcia-Lozano, Hiram, and Vladimir L. Kharitonov. "NUMERICAL COMPUTATION OF TIME DELAY LYAPUNOV MATRICES." IFAC Proceedings Volumes 39, no. 10 (2006): 60–65. http://dx.doi.org/10.3182/20060710-3-it-4901.00011.

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25

Balasuriya, Sanjeeva. "Uncertainty in finite-time Lyapunov exponent computations." Journal of Computational Dynamics 7, no. 2 (2020): 313–37. http://dx.doi.org/10.3934/jcd.2020013.

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26

Zhang, Bin, and Yingmin Jia. "Time-Varying Lyapunov Function for Mechanical Systems." Proceedings of International Conference on Artificial Life and Robotics 24 (January 10, 2019): 395–98. http://dx.doi.org/10.5954/icarob.2019.os14-3.

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27

Ghavimi, A. R., and A. J. Laub. "Residual bounds for discrete-time Lyapunov equations." IEEE Transactions on Automatic Control 40, no. 7 (July 1995): 1244–49. http://dx.doi.org/10.1109/9.400485.

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28

YAO, TIAN-LIANG, HAI-FENG LIU, JIAN-LIANG XU, and WEI-FENG LI. "LYAPUNOV-EXPONENT SPECTRUM FROM NOISY TIME SERIES." International Journal of Bifurcation and Chaos 23, no. 06 (June 2013): 1350103. http://dx.doi.org/10.1142/s0218127413501034.

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Since all kinds of noise exist in signals from real-world systems, it is very difficult to exactly estimate Lyapunov exponents from this time series. In this paper, a novel method for estimating the Lyapunov spectrum from a noisy chaotic time series is presented. We consider the higher-order mappings from neighbors into neighbors, rather than the mappings from small displacements into small displacements as usual. The influence of noise on the second-order mappings is researched, and an averaging method is proposed to cope with this noise. The mappings equations of the underlying deterministic system can be obtained from the noisy data via the method, and then the Lyapunov spectrum can be estimated. We demonstrate the performance of our algorithm for three familiar chaotic systems, Hénon map, the generalized Hénon map and Lorenz system. It is found that the proposed method provides a reasonable estimate of Lyapunov spectrum for these three systems when the noise level is less than 20%, 10% and 7%, respectively. Furthermore, our method is not sensitive to the distribution types of the noise, and the results of our method become more accurate with the increase of the length of time series.

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29

Kharitonov, Vladimir L. "Approximate Lyapunov matrices for time-delay systems." IFAC-PapersOnLine 51, no. 14 (2018): 142–46. http://dx.doi.org/10.1016/j.ifacol.2018.07.213.

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30

Wolf, Alan, Jack B. Swift, Harry L. Swinney, and John A. Vastano. "Determining Lyapunov exponents from a time series." Physica D: Nonlinear Phenomena 16, no. 3 (July 1985): 285–317. http://dx.doi.org/10.1016/0167-2789(85)90011-9.

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31

Yang, Ying, and Guopei Chen. "Finite Time Stability of Stochastic Hybrid Systems." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/867189.

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This paper considers the finite time stability of stochastic hybrid systems, which has both Markovian switching and impulsive effect. First, the concept of finite time stability is extended to stochastic hybrid systems. Then, by using common Lyapunov function and multiple Lyapunov functions theory, two sufficient conditions for finite time stability of stochastic hybrid systems are presented. Furthermore, a new notion called stochastic minimum dwell time is proposed and then, combining it with the method of multiple Lyapunov functions, a sufficient condition for finite time stability of stochastic hybrid systems is given. Finally, a numerical example is provided to illustrate the theoretical results.

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32

Mukdasai, Kanit, and Piyapong Niamsup. "An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales." Abstract and Applied Analysis 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/860506.

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We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, -uniform stability, andh-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

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33

Wu, Yuxiang, Tian Xu, and Hongqiang Mo. "Adaptive tracking control for nonlinear time-delay systems with time-varying full state constraints." Transactions of the Institute of Measurement and Control 42, no. 12 (March 6, 2020): 2178–90. http://dx.doi.org/10.1177/0142331220908987.

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This paper presents an adaptive tracking control approach for a class of uncertain nonlinear strict-feedback systems subject to time-varying full state constraints and time-delays. To stabilize such systems, an adaptive tracking controller is structured by combining the neural networks and the backstepping technique. To guarantee all states do not violate the time-varying constraint sets, the appropriate time-varying Barrier Lyapunov functions are employed at each stage of the backstepping procedure. By using the Lyapunov-Krasovskii functionals, the effect of time delay is eliminated. It is proved that the output follows the desired signal well without violating any constraints, and all the signals in the closed-loop system are semiglobal uniformly ultimately bounded by using the Lyapunov analysis. Finally, a comparison study simulation is provided to illustrate the effectiveness of the proposed control strategy.

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34

Polyakov, Andrey, Denis Efimov, and Wilfrid Perruquetti. "Finite-time and fixed-time stabilization: Implicit Lyapunov function approach." Automatica 51 (January 2015): 332–40. http://dx.doi.org/10.1016/j.automatica.2014.10.082.

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35

Xue, Bingxin, Ruihua Wang, and Shumin Fei. "Time-varying H∞ filtering for discrete-time switched systems with admissible edge-dependent average dwell time." Transactions of the Institute of Measurement and Control 42, no. 14 (June 19, 2020): 2719–32. http://dx.doi.org/10.1177/0142331220928889.

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This paper addresses the [Formula: see text] filtering problem for a class of discrete-time switched systems by using an admissible edge-dependent average dwell time (AED-ADT) method. By means of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is constructed, which can loosen the restrictions of Lyapunov function at switching points and interval interior points. Based on the MPCLF approach, sufficient conditions are established such that the filtering error system is globally uniformly exponentially stable (GUES) and a prescribed noise attenuation level in an [Formula: see text] sense is achieved. Moreover, the corresponding time-varying [Formula: see text] filters are given as well. Finally, the results of the simulation illustrate the feasibility and effectiveness of the proposed approaches.

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36

Li, Xiaodi, Xueyan Yang, and Shiji Song. "Lyapunov conditions for finite-time stability of time-varying time-delay systems." Automatica 103 (May 2019): 135–40. http://dx.doi.org/10.1016/j.automatica.2019.01.031.

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37

Duda, Józef. "A Lyapunov functional for a system with a time-varying delay." International Journal of Applied Mathematics and Computer Science 22, no. 2 (June 1, 2012): 327–37. http://dx.doi.org/10.2478/v10006-012-0024-7.

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A Lyapunov functional for a system with a time-varying delay The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval time-varying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

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38

Alastruey, Carlos F., and Manuel de la Sen. "Stability of time-delay systems via Lyapunov functions." Mathematical Problems in Engineering 8, no. 3 (2002): 197–205. http://dx.doi.org/10.1080/10241230215287.

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In this paper, a Lyapunov function candidate is introduced for multivariable systems with inner delays, without assuminga prioristability for the nondelayed subsystem. By using this Lyapunov function, a controller is deduced. Such a controller utilizes an input–output description of the original system, a circumstance that facilitates practical applications of the proposed approach.

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39

Du, Nguyen Huu, and Nguyen Chi Liem. "LINEAR TRANSFORMATIONS AND FLOQUET THEOREM FOR LINEAR IMPLICIT DYNAMIC EQUATIONS ON TIME SCALES." Asian-European Journal of Mathematics 06, no. 01 (March 2013): 1350004. http://dx.doi.org/10.1142/s1793557113500046.

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This paper is concerned with Cauchy problem, Lyapunov transformations, Floquet and Lyapunov theorems for linear implicit dynamic equation AtxΔ= Btx with index-1 on time scales. The stability of this equation under the act of these Lyapunov transformations is also considered. The results are a unification and generalization of previous results for differential-algebraic equations and implicit difference systems.

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40

Duda, J. "A Lyapunov functional for a neutral system with a time-varying delay." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 4 (December 1, 2013): 911–18. http://dx.doi.org/10.2478/bpasts-2013-0098.

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Abstract The paper presents a method of determining of the Lyapunov functional for a linear neutral system with an interval time-varying delay. The Lyapunov functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the trajectory of the system with a time-varying delay. The presented method gives analytical formulas for the coefficients of the Lyapunov functional

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41

Ghanmi, Boulbaba. "Partial stability analysis of nonlinear time-varying impulsive systems." International Journal of Biomathematics 12, no. 06 (August 2019): 1950066. http://dx.doi.org/10.1142/s1793524519500669.

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This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

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42

Zhu, Huayong, Yirui Cong, Xiangke Wang, Daibing Zhang, and Qingjie Zhang. "Consensusabilization for Continuous-Time High-Order Multiagent Systems with Time-Varying Delays." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/527039.

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For the consensus problems of high-order linear multiagent systems with time-varying delays in directed topologies, the LMI based-consensus criterion and NLMI-based consensusabilization (protocol parameters design that makes the multiagent systems achieve consensus) are investigated. Improved Lyapunov-Krasovskii functional is used for establishing the consensus convergence criteria and deriving the corresponding consensus protocol. In order to reduce the conservativeness, some proper free-weighting matrices are added into the derivative of Lyapunov-Krasovskii functional and that only keeps one necessary zoom. The numerical and simulation examples are given to demonstrate the effectiveness of the theoretical results. Compared with existing literatures, the convergence criterion and protocol design proposed have lower conservativeness.

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43

DÍAZ-SIERRA, R., and V. FAIRÉN. "NEW METHOD FOR THE ESTIMATION OF DOMAINS OF ATTRACTION OF FIXED POINTS FROM LYAPUNOV FUNCTIONS." International Journal of Bifurcation and Chaos 12, no. 11 (November 2002): 2467–77. http://dx.doi.org/10.1142/s0218127402005984.

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The estimation of the domain of stability of fixed points of nonlinear differential systems constitutes a practical problem of much interest in engineering. The procedures based on Lyapunov's second method configures an alternative worth consideration. It has the appeal of reducing calculation complexity and is time-saving with respect to the direct, computer crunching approach which requires a systematic numerical integration of the evolution equations from a gridlike pattern of initial conditions. However, it is not devoid of problems inasmuch as the Lyapunov function itself is problem-dependent and relies too much on presumptions. Additionally, the evaluation of its corresponding domain is produced in terms of a nonlinear programming problem with inequality constraints the resolution of which may sometimes require a large investment in computer time. These problems are in part avoided by restricting to quadratic Lyapunov functions, with the possible obvious consequence of limiting the estimation of the domain. In order to simplify the estimation of domains we exploit here a novel formulation of the issue of stability of invariant surfaces within Lyapunov's direct method [Díaz-Sierra et al., 2001]. The resulting method addresses directly the optimization problem associated to the evaluation of the stability domain. The problem is recast in a new, simpler form by playing both on the Lyapunov function itself and on the constraints. The gains from the procedure permit to conceive increased returns in the application of Lyapunov's direct method once it is realized that it is not prohibitive from a computational point of view to depart from the limited quadratic Lyapunov functions.

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44

Boonpikum, Aphirak, Thongchai Botmart, Piyapong Niamsup, and Wajaree Weera. "Improved Delay-Dependent Stability Criterion for Genetic Regulatory Networks with Interval Time-Varying Delays via New Lyapunov Functionals." Mathematical Problems in Engineering 2020 (October 21, 2020): 1–24. http://dx.doi.org/10.1155/2020/9590582.

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In this work, the stability analysis problem of the genetic regulatory networks (GRNs) with interval time-varying delays is presented. In the previous works, the constructions of Lyapunov functional have usually been in simple Lyapunov functional, augmented Lyapunov functional, and multiple integral Lyapunov functional. Therefore, we introduce new Lyapunov functionals expressed in terms of delay product functions. New delay-dependent sufficient conditions for the genetic regulatory networks (GRNs) are established in the terms of linear matrix inequalities (LMIS). In addition, a numerical example is provided to illustrate the effectiveness of the theoretical results.

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45

Lekgari, Mokaedi V. "Subgeometric Ergodicity under Random-Time State-Dependent Drift Conditions." Journal of Probability and Statistics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/519276.

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Motivated by possible applications of Lyapunov techniques in the stability of stochastic networks, subgeometric ergodicity of Markov chains is investigated. In a nutshell, in this study we take a look atf-ergodic general Markov chains, subgeometrically ergodic at rater, when the random-time Foster-Lyapunov drift conditions on a set of stopping times are satisfied.

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46

Kharitonov *, V. L. "Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case." International Journal of Control 78, no. 11 (July 20, 2005): 783–800. http://dx.doi.org/10.1080/00207170500164837.

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47

He, Jianbin, Simin Yu, and Jianping Cai. "Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems." International Journal of Bifurcation and Chaos 26, no. 13 (December 15, 2016): 1650219. http://dx.doi.org/10.1142/s0218127416502199.

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Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.

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48

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 asymptotically stable are established, then the disturbance attenuation properties in the sense ofL2gain are studied. The main advantage of discretized Lyapunov function approach is that the derived sufficient conditions are convex in subsystem matrices, which makes the analysis results easily used and generalized. Thus, theH∞control synthesis problem is considered. On the basis of analysis results in hand, the control synthesis procedures including both controller and switching law design are unified into one-step method which explicitly facilitates the control synthesis process. Several numerical examples are provided to illustrate the results within our paper.

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49

Cao Xiao-Qun, Song Jun-Qiang, Ren Kai-Jun, Leng Hong-Ze, and Yin Fu-Kang. "Highly accurate computation of finite-time Lyapunov exponent." Acta Physica Sinica 63, no. 18 (2014): 180504. http://dx.doi.org/10.7498/aps.63.180504.

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50

Polyakov, A., D. Efimov, and W. Perruquetti. "Finite-time Stabilization Using Implicit Lyapunov Function Technique." IFAC Proceedings Volumes 46, no. 23 (2013): 140–45. http://dx.doi.org/10.3182/20130904-3-fr-2041.00043.

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