Finite-time Asynchronous Control for semi-Markov Jump Systems with Random Uncertainties and Actuator Faults

Abstract

This article is aimed at studying the finite-time reliable asynchronous control issue for continuous semi-Markov jump systems (S-MJSs) with actuator failures and randomly occurring uncertainties (ROUs). To characterize the asynchronous phenomenon between the system mode and the controller mode, the mode detector approach via a hidden semi-Markov model (HSM) is adopted. The transition probability (TP) matrix of the HSM is nonhomogeneous, which can be provided by a polytopic structure. By resorting the mode-dependent Lyapunov function, sufficient conditions are attained to guarantee the stochastic finite-time boundedness (SFTB) and H∞ performance of the closed-loop system. Then, according to a skillful matrix inequality transforming method, the reliable asynchronous control law is constructed. Finally, a tunnel diode circuit system and a mass-spring-damper mechanical system are proposed to demonstrate the superiority, effectiveness and practicality of the developed design method.