SMC for Discrete Singular Semi‐Markov Switching Systems With Bilateral Dwell Time

ABSTRACT This work investigates the sliding mode control (SMC) for discrete singular semi‐Markov switching systems with bilateral dwell time (DT). Bilateral DT constraints are explicitly incorporated into the stability analysis, thus generalizing the existing results under unilateral constraints. Owing to time‐varying singular matrix in the system, a stable state feedback strategy is designed in the controller design. The stability behavior of singular semi‐Markov switching systems in mean‐square sense is analyzed based on the Lyapunov function. The main challenge of this paper is to introduce the singular matrix into the system and the sliding surface, and thus to construct a feasible controller under bilateral DT. By utilizing semi‐Markov kernel method for eliminating the matrix power, new sufficient conditions with multiple inequality conditions are introduced for mean‐square stability. Furthermore, a novel SMC approach is designed to improve the dynamic performance of the discrete model, and the reachability of quasi‐sliding mode is achieved. Finally, the DC motor is introduced to demonstrate the validity of the proposed method.