Asynchronous sliding‐mode control for two‐dimensional nonlinear Markov jump systems with time‐varying delays

Abstract Based on the Roesser model, the asynchronous sliding‐mode control (SMC) problem for two‐dimensional (2‐D) Markov jump systems (MJSs) with time‐varying delays is studied in this article. Since the controller mode cannot always access the system mode, the asynchronous phenomenon between the system mode and the controller mode will be described by the hidden Markov model (HMM). First, under the framework of HMM, the asynchronous 2D‐SMC law is designed based on 2‐D sliding surface function to ensure closed‐loop 2‐D discrete MJSs asymptotic mean square stability and the reachability of sliding regions around specific sliding surfaces. Second, an algorithm for deducing the law of 2‐D asynchronous SMC is presented. Finally, a numerical example is given to verify the effective of the results.