Robust adaptive sliding mode control for delayed singular systems with randomly occurring uncertainty: the uncertain probability case

In this paper, the adaptive sliding mode control (SMC) problem is discussed for a class of discrete singular systems subject to time-varying delays and randomly occurring uncertainty, where the uncertain occurrence probability case and the nonlinear disturbance are addressed. A proper discrete switching function is firstly designed and the corresponding sliding mode dynamics is obtained. The aim of the addressed problem is to design an adaptive controller such that, for all randomly occurring parameter uncertainty, nonlinear disturbances and time-varying delays, the closed-loop system is guaranteed to be regular, causal and stable under uncertain occurrence probability case. In particular, a robust adaptive sliding mode control (RASMC) law is constructed which is capable of ensuring the reachability of the pre-specified sliding surface. Finally, the feasibility of the proposed RASMC approach is illustrated by numerical simulations.