Robust resilient controller design for uncertain discrete-time fuzzy Markovian jump delayed systems

This paper investigates the problem of robust stabilization for a class of nonlinear discrete-time Markovian jump delayed systems using the Takagi-Sugeno ( T-S ) fuzzy model approach. The time delays are assumed to be time-varying and related to the mode, especially their bounds are also mode-dependent. Our aim is to design a resilient fuzzy Markovian switched controller such that the resulting closed-loop system is robustly stochastically stable. Based on an improved Markovian switched fuzzy-basis-dependent Lyapunov functional, some delay-dependent conditions for the solvability of this problem are derived in terms of relaxed linear matrix inequalities ( LMIs ), the desired resilient fuzzy controller can be designed through solving these LMIs. A numerical example is provided to illustrate the effectiveness of the proposed approach.

[1]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[2]  Shengyuan Xu,et al.  Delay-dependent stabilization for stochastic fuzzy systems with time delays , 2007, Fuzzy Sets Syst..

[3]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[4]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[5]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[6]  Tong Heng Lee,et al.  $H_{\infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach , 2008, IEEE Transactions on Fuzzy Systems.

[7]  Tao Li,et al.  Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function , 2005, Fuzzy Sets Syst..

[8]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[9]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[10]  Shengyuan Xu,et al.  Fuzzy H ∞ filtering for nonlinear Markovian jump neutral systems , 2011, Int. J. Syst. Sci..

[11]  Shengyuan Xu,et al.  Delay‐dependent robust stabilization for uncertain stochastic switching systems with distributed delays , 2009 .

[12]  Vilma Alves de Oliveira,et al.  Robust $H_{\infty}$ Fuzzy Control Approach for a Class of Markovian Jump Nonlinear Systems , 2006, IEEE Transactions on Fuzzy Systems.

[13]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[14]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[15]  Peng Shi,et al.  Robust filtering for jumping systems with mode-dependent delays , 2006, Signal Process..

[16]  Guang-Hong Yang,et al.  An LMI-based Approach for State Feedback Controller Design of Markovian Jump Nonlinear Systems , 2007, 2007 IEEE International Conference on Control Applications.

[17]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[18]  Huijun Gao,et al.  Stabilization of Networked Control Systems With a New Delay Characterization , 2008, IEEE Transactions on Automatic Control.

[19]  M. Mahmoud,et al.  Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities , 2002 .

[20]  E. Boukas,et al.  Robust H∞ control for linear Markovian jump systems with unknown nonlinearities , 2003 .

[21]  P. Shi,et al.  Robust H1 control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach , 2007 .

[22]  Gang Feng,et al.  H∞ control of uncertain dynamical fuzzy discrete-time systems , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[23]  Kazuo Tanaka,et al.  A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer , 1994, IEEE Trans. Fuzzy Syst..

[24]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[25]  Qing Wang,et al.  H∞Model Approximation for Discrete-time Markovian Jump Systems with Mode-dependent Time Delays , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[26]  Huai-Ning Wu.  Delay-dependent H∞ fuzzy observer-based control for discrete-time nonlinear systems with state delay , 2008, Fuzzy Sets Syst..