Sliding Mode Control for Markov Jump Singularly Perturbed Systems Under Piecewise Homogeneous Stochastic Communication Protocol

This work involves the sliding mode control (SMC) issue for a class of Markov jump singularly perturbed systems (MJSPSs) under consideration of unmatched external disturbances and communication constraints. For the first time, the piecewise homogeneous Markov chain (MC) which depends on the system mode and the controller mode is applied to control the scheduling of stochastic communication protocol (SCP), so that the MCs in the system models, the controller and the SCP constitute a three-layer nonstationary Markov model (NMM). This model perfectly describes the different objects of the three MCs and reflects the mutual regulation among them. The critical issue is to devise an adaptive controller and a sliding surface (SS) simultaneously under SCP scheduling. By applying a standard singular sliding mode surface, an appropriate nonstationary SMC law is established to promise the accessibility of the SS and the stability of the closed-loop system (CLS), and meet the expected performance indicator. Further, using the mode-dependent Lyapunov function and piecewise homogeneous Markov model method, sufficient criteria are obtained. The specific expression of the control gain is obtained by matrix decoupling technology. Finally, a numerical simulation is furnished to testify the correctness of the conclusion.