A switching asynchronous control approach for Takagi-Sugeno fuzzy Markov jump systems with time-varying delay

Likui Wang, Yinghong Zhao, Xiangpeng Xie, Hak-Keung Lam

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Till now, most of the results on T-S (Takagi-Sugeno) fuzzy Markov jump systems are synchronous and independent of the analysis of membership functions (MFs), which leads to conservatism. Therefore, it is significant to study the MFs-dependent Lyapunov-Krasovskii functional (LKF) while consid-ering asynchrony. This article investigates the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> control issue of T-S fuzzy Markov jump systems with time-varying delay. First, delay-product-type (DPT) terms and MFs are introduced to design a new LKF, which fully utilizes the information of time-varying delay and MFs simultaneously. Moreover, based on a hidden Markov model, the controller mode is assumed to operate asynchronously with the system mode, and an asynchronous switching fuzzy controller is proposed by employing the switching approach. Thus a more practical and less conservative stability criterion is obtained to ensure the closed-loop system is stochas-tically stable with <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance. Finally, three examples are provided to illustrate the superiority and practicability of the presented method.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalIEEE Transactions on Fuzzy Systems
Publication statusAccepted/In press - 1 Aug 2023

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