Stability Analysis of Delayed Discrete Singular Piecewise Homogeneous Markovian Jump Systems With Unknown Transition Probabilities via Sliding-Mode Approach

In this article, the sliding-mode control (SMC) strategy is outlined for discrete-time singular Markovian jump systems with time-varying delays and time-varying transition probabilities (TPs). To simplify the complexities arising from the time-varying TPs in the Markov chain, the TPs in this study are reasonably considered to be finite piecewise-homogeneous. The variations of TPs are stochastic and governed by a higher level transition probability (HTP) matrix. It is acceptable for both the TP matrix and HTP matrix to be partly unknown, which makes the system closer to reality and more complex to investigate. In this context, our goal lies in constructing a common sliding-mode surface to avoid the effects of switching among sequential subsystems and piecewise homogeneous TPs on the convergence of the sliding-mode surface. Additionally, we aim to design an appropriate SMC law to guarantee the reachability of the quasi-sliding mode in a finite-time interval. Through the linear matrix inequalities, sufficient criteria are offered to make the closed-loop dynamic system stochastically admissible. Finally, the numerical result will show that the presented SMC strategy is valid.