New Stabilization Results for Semi-Markov Chaotic Systems with Fuzzy Sampled-Data Control

This paper investigates the problem of stabilization for semi-Markov chaotic systems with fuzzy sampled-data controllers, in which the semi-Markov jump has generally uncertain transition rates. The exponential stability condition is firstly obtained by the following two main techniques: To make full use of the information about the actual sampling pattern, a novel augmented input-delay-dependent Lyapunov–Krasovskii functional (LKF) is firstly introduced. Meanwhile, a new zero-value equation is established to increase the combinations of component vectors of the resulting vector. The corresponding fuzzy sampled-data controllers are designed based on the stability condition. Finally, the validity and merits of the developed theories are shown by two numerical examples.

[1]  Xin-Ping Guan,et al.  Adaptive fuzzy control for chaotic systems with H[infin] tracking performance , 2003, Fuzzy Sets Syst..

[2]  Hong Wang,et al.  Stabilization of chaotic systems under variable sampling and state quantized controller , 2017, Fuzzy Sets Syst..

[3]  Yongkun Li,et al.  Improved stability and H∞ performance for neutral systems with uncertain Markovian jump , 2016 .

[4]  Corentin Briat,et al.  Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints , 2016, Autom..

[5]  Bao-Zhu Guo,et al.  Non-fragile H∞ filtering for delayed Takagi-Sugeno fuzzy systems with randomly occurring gain variations , 2017, Fuzzy Sets Syst..

[6]  Kaibo Shi,et al.  A new method for quantized sampled-data synchronization of delayed chaotic Lur’e systems , 2019 .

[7]  Xiaofeng Liao,et al.  Impulsive control for T-S fuzzy model based chaotic systems with adaptive feedback , 2009, 2009 International Conference on Communications, Circuits and Systems.

[8]  Yajuan Liu,et al.  Asynchronous output feedback dissipative control of Markovian jump systems with input time delay and quantized measurements , 2019, Nonlinear Analysis: Hybrid Systems.

[9]  Hak-Keung Lam,et al.  Stabilization of Chaotic Systems Using Linear sampled-Data Controller , 2007, Int. J. Bifurc. Chaos.

[10]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

[11]  Jin Bae Park,et al.  An improved digital redesign for sampled-data fuzzy control systems: Fuzzy Lyapunov function approach , 2017, Inf. Sci..

[12]  José Manoel Balthazar,et al.  On an optimal control design for Rössler system , 2004 .

[13]  Shouming Zhong,et al.  New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems , 2018, Nonlinear Analysis: Hybrid Systems.

[14]  Zhongjie Wang,et al.  Stability of Markovian jump systems with generally uncertain transition rates , 2013, J. Frankl. Inst..

[15]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[16]  Corentin Briat.  Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints , 2013, Autom..

[17]  Xinzhi Liu,et al.  A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems , 2017, Fuzzy Sets Syst..

[18]  Wen Yu.  Passive equivalence of chaos in Lorenz system , 1999 .

[19]  Yueying Wang,et al.  Reliable Fuzzy Tracking Control of Near-Space Hypersonic Vehicle Using Aperiodic Measurement Information , 2019, IEEE Transactions on Industrial Electronics.

[20]  Jinde Cao,et al.  Exponential passivity conditions on neutral stochastic neural networks with leakage delay and partially unknown transition probabilities in Markovian jump , 2018, Advances in Difference Equations.

[21]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[22]  Peng Shi,et al.  Sampled-Data Fuzzy Control of Chaotic Systems Based on a T–S Fuzzy Model , 2014, IEEE Transactions on Fuzzy Systems.

[23]  Dong Yue,et al.  An Improved Input Delay Approach to Stabilization of Fuzzy Systems Under Variable Sampling , 2012, IEEE Transactions on Fuzzy Systems.

[24]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Ju H. Park,et al.  Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control , 2018, IEEE Transactions on Fuzzy Systems.

[26]  Jinde Cao,et al.  New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters , 2018, J. Frankl. Inst..

[27]  Ju H. Park,et al.  New Methods of Fuzzy Sampled-Data Control for Stabilization of Chaotic Systems , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[28]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[29]  Shih-Yu Li,et al.  Adaptive synchronization of complicated chaotic systems with uncertainties via fuzzy modeling-based control strategy , 2018, Inf. Sci..

[30]  Yang Liu,et al.  T-S fuzzy model-based impulsive control for chaotic systems and its application , 2011, Math. Comput. Simul..

[31]  Huai-Ning Wu,et al.  On Fuzzy Sampled-Data Control of Chaotic Systems Via a Time-Dependent Lyapunov Functional Approach , 2015, IEEE Transactions on Cybernetics.

[32]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[33]  Kazuo Tanaka,et al.  A unified approach to controlling chaos via an LMI-based fuzzy control system design , 1998 .

[34]  Zhipeng Qiu,et al.  Stochastic stability criterion of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump , 2019, Neurocomputing.

[35]  Jing-Wen Yi,et al.  Exponential synchronization of complex dynamical networks with markovian jump parameters and stochastic delays and its application to multi-agent systems , 2013, Commun. Nonlinear Sci. Numer. Simul..

[36]  Hamid Reza Karimi,et al.  Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems , 2018, IEEE Transactions on Fuzzy Systems.

[37]  Victor Sreeram,et al.  Fuzzy-Model-Based Nonfragile Control for Nonlinear Singularly Perturbed Systems With Semi-Markov Jump Parameters , 2018, IEEE Transactions on Fuzzy Systems.

[38]  Shouming Zhong,et al.  A New Approach to Stabilization of Chaotic Systems With Nonfragile Fuzzy Proportional Retarded Sampled-Data Control , 2019, IEEE Transactions on Cybernetics.

[39]  Xinzhi Liu,et al.  Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities , 2012, J. Frankl. Inst..

[40]  Shouming Zhong,et al.  Novel master-slave synchronization criteria of chaotic Lur'e systems with time delays using sampled-data control , 2017, J. Frankl. Inst..

[41]  Zhi-Hong Guan,et al.  Impulsive synchronization for Takagi-Sugeno fuzzy model and its application to continuous chaotic system [rapid communication] , 2005 .

[42]  Jun Yoneyama,et al.  Robust H∞ control of uncertain fuzzy systems under time-varying sampling , 2010, Fuzzy Sets Syst..

[43]  Shouming Zhong,et al.  Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays , 2017, Appl. Math. Comput..

[44]  Peng Shi,et al.  Stability and Stabilization of a Class of Discrete-Time Fuzzy Systems With Semi-Markov Stochastic Uncertainties , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[45]  Feng Li,et al.  Finite-time H∞ synchronization control for semi-Markov jump delayed neural networks with randomly occurring uncertainties , 2015, Neurocomputing.

[46]  Yuanqing Xia,et al.  Fuzzy-Model-Based Sampled-Data Control of Chaotic Systems: A Fuzzy Time-Dependent Lyapunov–Krasovskii Functional Approach , 2017, IEEE Transactions on Fuzzy Systems.

[47]  Huaicheng Yan,et al.  Input–output finite-time mean square stabilization of nonlinear semi-Markovian jump systems , 2019, Automatica.

[48]  Yan-Wu Wang,et al.  Distributed Control of Nonlinear Multiagent Systems With Unknown and Nonidentical Control Directions via Event-Triggered Communication , 2020, IEEE Transactions on Cybernetics.

[49]  Aizhong Lei,et al.  Impulse tuning of Chua chaos , 2005 .

[50]  Kok Lay Teo,et al.  Sampled-data synchronization control for chaotic neural networks subject to actuator saturation , 2017, Neurocomputing.

[51]  H. Wang,et al.  An LMI-based stable fuzzy control of nonlinear systems and its application to control of chaos , 1996, Proceedings of IEEE 5th International Fuzzy Systems.