Learning-based asynchronous sliding mode control for semi-Markov jump systems with time-varying delay using relaxed negative-determination lemma

Abstract

This article figures out the asynchronous sliding mode control (SMC) issue for a class of semi-Markov jump systems (SMJSs) with time-varying delay and actuator faults. Firstly, to tackle the chattering produced by asynchronous phenomenon and guarantee smooth reachability, the hidden Markov model and the reduced-order theory are used to design the learning-based SMC law. Besides, the mode-dependent augmented Lyapunov–Krasovskii functional (LKF) is constructed. By using the relaxed negative definite lemma and the generalized free matrix integral inequality (GFMBII), sufficient conditions for ensuring the stochastic stability of the SMJSs are provided. Furthermore, the conservatism of the maximum time delay is effectively reduced by adjusting the value of β. Finally, simulation examples prove the validity and superiority of the proposed method.