Sliding Mode Output Feedback Controller Design of Discrete-Time Markov Jump System Based on Hidden Markov Model Approach

This paper investigates the problem of sliding mode controller design based on output feedback for discrete-time Markov jump systems. Considering the typical asynchronous phenomenon for jump systems, here we adopt the Hidden Markov Model (HMM) to quantify the asynchronous degree. Based on this, a static output feedback sliding surface is constructed. Sufficient conditions in terms of bilinear matrix inequalities are proposed ensuring the sliding motion dynamic to be stochastically stable and its $\mathcal {H}_\infty $ performance for the considered discrete time Markov jump systems. Moreover, the reachability of the sliding mode surface is ensured by a predesigned control law. The whole design scheme is presented by using an iterative algorithm. Finally, simulation results are presented to illustrate the effectiveness of the design methodology