Stability and Stabilization of Discrete-Time T-S Fuzzy Systems With Stochastic Perturbation and Time-Varying Delay

• Published in: IEEE transactions on fuzzy systems Vol. 22; no. 1; pp. 124 - 138
• Main Authors: Yang, Xiaozhan, Wu, Ligang, Lam, Hak-Keung, Su, Xiaojie
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Delay; Delay partitioning; Delays; Fuzzy systems; Mathematical analysis; Mathematical models; Perturbation methods; Stability; Stability analysis; Stabilization; stochastic perturbation; Stochastic processes; Stochastic systems; Stochasticity; Symmetric matrices; Takagi-Sugeno (T-S) fuzzy systems; time-varying delay; Time-varying systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2013.2249518

This paper is concerned with the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation and time-varying state delay. By means of the delay-partitioning method and slack variables, a novel fuzzy Lyapunov-Krasovskii function is constructed to reduce the conservatism of stability conditions. Those conditions are converted to finite linear matrix inequalities, which can be readily solved by standard numerical software. Then, the delay-dependent stabilization approach, which is based on a nonparallel distributed compensation scheme, is introduced for the closed-loop fuzzy systems. Finally, illustrative examples are provided to illustrate the feasibility and effectiveness of the proposed methods.