New Results on $H_\infty$ Filter Design for Nonlinear Systems With Time Delay via T–S Fuzzy Models

This paper focuses on the problem of designing H∞ filters for nonlinear systems with time-varying delay via Takagi-Sugeno (T-S) fuzzy models. Some new results on H∞ filter design are proposed by estimating the upper bounds of the derivatives of Lyapunov functionals without ignoring some useful terms, which improve the existing ones. In addition, a sufficient condition for the existence of such an H∞ filter is established in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, two examples are given to demonstrate the effectiveness of the proposed method.

[1]  Huaguang Zhang,et al.  Fuzzy $H_\infty$ Filter Design for a Class of Nonlinear Discrete-Time Systems With Multiple Time Delays , 2007, IEEE Transactions on Fuzzy Systems.

[2]  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.

[3]  Yuanqing Xia,et al.  New Results on H∞ Filtering for Fuzzy Time-Delay Systems , 2009, IEEE Trans. Fuzzy Syst..

[4]  Jinliang Liu,et al.  H∞ filter design for nonlinear systems with time-delay through T-S fuzzy model approach , 2010, 2010 Chinese Control and Decision Conference.

[5]  Huaguang Zhang,et al.  A new fuzzy H∞ filter design for nonlinear continuous-time dynamic systems with time-varying delays , 2009, Fuzzy Sets Syst..

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

[7]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[8]  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.

[9]  Yong-Yan Cao,et al.  Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models , 2001, Fuzzy Sets Syst..

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

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

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

[13]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

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

[15]  Emilia Fridman,et al.  A new H∞ filter design for linear time delay systems , 2001, IEEE Trans. Signal Process..

[16]  Xiqin He,et al.  Some Sufficient Stability Conditions on T-S Fuzzy Systems with Time-Delay , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[17]  D. Bernstein,et al.  Steady-state kalman filtering with an H∞ error bound , 1989, 1989 American Control Conference.

[18]  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.

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

[20]  E. Sánchez,et al.  OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS , 2007 .

[21]  D. Bernstein,et al.  Steady-state Kalman filtering with an H ∞ error bound , 1989 .

[22]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

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

[24]  Emilia Fridman,et al.  An improved delay-dependent H∞ filtering of linear neutral systems , 2004, IEEE Trans. Signal Process..

[25]  Bing Chen,et al.  Reliable control design of fuzzy dynamic systems with time-varying delay , 2004, Fuzzy Sets Syst..

[26]  Michael V. Basin,et al.  Optimal Filtering for Linear System States over Polynomial Observations , 2006, First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC'06).

[27]  Michael Basin.  Optimal Filtering for Polynomial Systems , 2008 .