$H_{\infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach

This paper is concerned with the Hinfin filter design for nonlinear systems with time-varying delay via Takagi-Sugeno fuzzy model approach. Delay-dependent design method is proposed in terms of linear matrix inequalities (LMIs), which forms the main contribution of this paper. The main technique used is the free-weighting matrix method combined with a matrix decoupling approach. The results for rate-independent case, delay-independent case, and delay-free case are also given as easy corollaries. An illustrative example is given to show the effectiveness of the present method.

[1]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[3]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[4]  Jong Hae Kim,et al.  Output feedback robust H∞ control of uncertain fuzzy dynamic systems with time-varying delay , 2000, IEEE Trans. Fuzzy Syst..

[5]  Yong-Yan Cao,et al.  Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach , 2000, IEEE Trans. Fuzzy Syst..

[6]  Bor-Sen Chen,et al.  H∞ fuzzy estimation for a class of nonlinear discrete-time dynamic systems , 2001, IEEE Trans. Signal Process..

[7]  Kazuo Tanaka,et al.  Fuzzy control systems design and analysis , 2001 .

[8]  Fuwen Yang,et al.  Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises , 2002, IEEE Trans. Autom. Control..

[9]  Zhang Yi,et al.  Stability of fuzzy control systems with bounded uncertain delays , 2002, IEEE Trans. Fuzzy Syst..

[10]  Zidong Wang,et al.  Nonlinear filtering for state delayed systems with Markovian switching , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[11]  Huijun Gao,et al.  Delay-Dependent Robust and - Filtering for a Class of Uncertain Nonlinear Time-Delay Systems , 2003 .

[12]  P. Shi,et al.  Fuzzy Output Feedback Control Design for Nonlinear Systems: An LMI Approach , 2003 .

[13]  Huijun Gao,et al.  Delay-dependent robust H∞ and L2-L∞ filtering for a class of uncertain nonlinear time-delay systems , 2003, IEEE Trans. Autom. Control..

[14]  Andreas Antoniou,et al.  A near-optimal multiuser detector for DS-CDMA systems using semidefinite programming relaxation , 2003, IEEE Trans. Signal Process..

[15]  Peng Shi,et al.  H∞ fuzzy output feedback control design for nonlinear systems: an LMI approach , 2003, IEEE Trans. Fuzzy Syst..

[16]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[17]  E. Fridman,et al.  An improved delay-dependent H/sub /spl infin// filtering of linear neutral systems , 2004, IEEE Transactions on Signal Processing.

[18]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[19]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[20]  Lihua Xie,et al.  Robust filtering under stochastic parametric uncertainties , 2004, Autom..

[21]  Shengyuan Xu,et al.  Exponential H∞ filter design for uncertain Takagi-Sugeno fuzzy systems with time delay , 2004, Eng. Appl. Artif. Intell..

[22]  Xin-Ping Guan,et al.  Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays , 2004, IEEE Transactions on Fuzzy Systems.

[23]  Y.-C. Lin,et al.  Robust mixed H 2/H ∞ filtering for discrete-time delay fuzzy systems , 2005, Int. J. Syst. Sci..

[24]  Lihua Xie,et al.  New Approach to Mixed Filtering for Polytopic Discrete-Time Systems , 2005 .

[25]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[26]  Shengyuan Xu,et al.  Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers , 2005, IEEE Transactions on Fuzzy Systems.

[27]  Tong Heng Lee,et al.  Stabilization of uncertain fuzzy time-delay systems via variable structure control approach , 2005, IEEE Transactions on Fuzzy Systems.

[28]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[29]  James Lam,et al.  Parameter-dependent filter design with guaranteed H-infinity performance , 2005 .

[30]  Tong-heng Lee,et al.  Technical communique: Improvement on observer-based H∞ control for T-S fuzzy systems , 2005 .

[31]  Bor-Sen Chen,et al.  Robust Filtering for Nonlinear , 2005 .

[32]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[33]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[34]  Min Wu,et al.  An improved global asymptotic stability criterion for delayed cellular neural networks , 2006, IEEE Transactions on Neural Networks.

[35]  Qing-Guo Wang,et al.  Fuzzy Weighting-Dependent Approach to $H_{\infty}$ Filter Design for Time-Delay Fuzzy Systems , 2007, IEEE Transactions on Signal Processing.