A Switching Asynchronous Control Approach for Takagi-Sugeno Fuzzy Markov Jump Systems With Time-Varying Delay

Abstract

Till now, most of the results on Takagi–Sugeno (T-S) 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 considering asynchrony. This article investigates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><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 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 that the closed-loop system is stochastically stable with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><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.