Improved Approach to Robust H∞ Stabilization of Discrete-Time T-S Fuzzy Systems With Time-Varying Delays

This study is concerned with the robust stabilization problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. To improve the conditions for the solvability of the stabilization problem, a nonquadratic Lyapunov-Krasovskii functional with a triple-summation term is established, and a nonparallel distributed compensation (non-PDC) scheme is adopted along with the matrixtransformation technique. In addition, an appropriate free-weightingmatrix method is proposed to exploit novel slack variables for null sum terms, especially resulting from Σi (xi+1 - xi)T (·)(xi+1 + xi).

[1]  Shengyuan Xu,et al.  Robust H∞ control for uncertain fuzzy systems with distributed delays via output feedback controllers , 2008, Inf. Sci..

[2]  C. Peng,et al.  State feedback controller design of networked control systems with interval time‐varying delay and nonlinearity , 2008 .

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

[4]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[5]  Sung Hyun Kim,et al.  Networked-based robust Hinfinity control design using multiple levels of network traffic , 2009, Autom..

[6]  Dong Yue,et al.  STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY , 2006 .

[7]  Xiaoping Liu,et al.  Robust Hinfinity control of Takagi-Sugeno fuzzy systems with state and input time delays , 2009, Fuzzy Sets Syst..

[8]  Xinghuo Yu,et al.  Robust H/sub /spl infin// control for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay , 2005, Proceedings of the 2005, American Control Conference, 2005..

[9]  Pierre Apkarian,et al.  Parameterized linear matrix inequality techniques in fuzzy control system design , 2001, IEEE Trans. Fuzzy Syst..

[10]  Hideki Hashimoto,et al.  Trajectory Tracking by TP Model Transformation: Case Study of a Benchmark Problem , 2007, IEEE Transactions on Industrial Electronics.

[11]  Qing-Long Han,et al.  Robust $H_{\infty}$ Control for Uncertain Takagi–Sugeno Fuzzy Systems With Interval Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

[12]  Engang Tian,et al.  Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay , 2008, Fuzzy Sets Syst..

[13]  Friedemann Leibfritz,et al.  An LMI-Based Algorithm for Designing Suboptimal Static H2/Hinfinity Output Feedback Controllers , 2000, SIAM J. Control. Optim..

[14]  James Lam,et al.  Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Shengyuan Xu,et al.  Delay-Dependent Robust $\hbox{\it H}_\infty$ Control for Uncertain Discrete-Time Fuzzy Systems With Time-Varying Delays , 2009, IEEE Transactions on Fuzzy Systems.

[16]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[17]  Jun Yoneyama,et al.  Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays , 2008, Inf. Sci..

[18]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[19]  Jun Yoneyama,et al.  New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems , 2007, IEEE Transactions on Fuzzy Systems.

[20]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[21]  PooGyeon Park,et al.  Stability and robust stability for systems with a time-varying delay , 2007, Autom..

[22]  Y. Tipsuwan,et al.  Network-based control systems: a tutorial , 2001, IECON'01. 27th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.37243).

[23]  Shaocheng Tong,et al.  Guaranteed cost control of T–S fuzzy systems with input delay , 2008 .

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

[25]  Qing-Long Han,et al.  On guaranteed cost fuzzy control for nonlinear systems with interval time-varying delay , 2007 .

[26]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[27]  Engang Tian,et al.  Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay , 2006, Fuzzy Sets Syst..

[28]  Han-Xiong Li,et al.  New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.