Finite-Time Asynchronous Switching Control for Fuzzy Markov Jump Systems by Applying Polynomial Membership Functions

This article addresses the problem of finite-time asynchronous switching control for fuzzy Markov jump systems (FMJSs) using polynomial membership functions. Firstly, a Lyapunov-Krasovskii functional (LKF) is designed, incorporating both system modes and polynomial membership functions. This LKF contains more information about the membership functions, closely aligning with the characteristics of FMJSs, and effectively reducing conservatism. Based on the polynomial matrices switching rule, a practical asynchronous switching controller is introduced. The objective is to ensure finite-time boundedness of the closed-loop FMJSs while satisfying a <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 index. Furthermore, the average dwell time method is applied to handle the switching signal, eliminating the predefined assumptions that switching numbers are finite or that system states are constrained to a specific region. Ultimately, the validity and practicability of the obtained results are verified through three examples.