Dissipativity Analysis and Synthesis for Discrete-Time T-S Fuzzy Stochastic SystemsWith Time-Varying Delay

• Published in: IEEE transactions on fuzzy systems Vol. 22; no. 2; pp. 380 - 394
• Main Authors: Wu, Ligang, Yang, Xiaozhan, Lam, Hak-Keung
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Delay; Dissipation; Dissipativity; Fuzzy systems; Mathematical models; model transformation; Perturbation methods; stochastic perturbation; Stochasticity; Synthesis; Takagi-Sugeno (T-S) fuzzy systems; time-varying delay; Transformations
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2013.2256913

This paper is concerned with the problems of dissipativity analysis and synthesis for discrete-time Takagi-Sugeno fuzzy systems with stochastic perturbation and time-varying delay. First, a novel model transformation method is introduced to pull the time-varying delay uncertainty out of the original system. Consequently, the transformed model is composed of a linear time-invariant system and a norm-bounded uncertain subsystem. By using this model transformation method combined with the Lyapunov-Krasovskii technique, sufficient conditions of the dissipativity are established. Then, a fuzzy controller is designed to guarantee the dissipative performance of the closed-loop system. Finally, three examples are presented: one shows the effectiveness of model transformation method, the second performs the comparison with alternative approaches, and the third illustrates the applicability of the proposed dissipative control methods.