Dual asynchronous control for T‐S fuzzy semi‐Markov jump systems: A finite‐time design

Abstract

This paper addresses the control problem of Takagi–Sugeno fuzzy semi‐Markov jump systems (TFSMJSs) under the finite‐time analysis and synthesis framework. Due to the commonly used networked communication structure, the semi‐Markovian jumping modes and fuzzy premise variables cannot always perfectly match for system and controller among the whole system operation. More precisely, both asynchronous phenomena in fuzzy membership and jumping mode are taken into account, and then, mode‐dependent finite‐time controllers are developed with these features. By utilizing stochastic analysis and Lyapunov–Krasovskii stability theory, sufficient criteria are first established for the closed‐loop system in the context of mean‐square sense. Furthermore, feedback controller gains are captured by the matrix technique and parallel distributed compensation (PDC)‐related arguments. Eventually, a simulation example of an unmanned marine vehicle (UMV) is utilized to demonstrate the validity of the developed results.