Robust adaptive sliding mode control for discrete singular systems with randomly occurring mixed time-delays under uncertain occurrence probabilities

Abstract

This paper is concerned with the problem of robust adaptive sliding mode control (RASMC) for discrete singular systems subject to randomly occurring mixed time-delays (ROMTDs) under uncertain occurrence probabilities. The mixed time delays are considered, which are comprised of both the discrete interval delays and infinite distributed delays. Meantime, two random variables obeying the Bernoulli distribution are utilised to depict the phenomena of randomly occurring discrete time-varying delay and distributed time-delay, in which the uncertain occurrence probabilities are modelled by the known scalars. An appropriate sliding surface function is firstly presented. Furthermore, some sufficient criteria via the free weighting matrices idea are obtained to ensure the admissibility of the resultant sliding motion by introducing new Lyapunov-Krasovskii functional. Subsequently, an RASMC law is synthesised to ensure the reachability criterion of pre-designed sliding surface, where an adaptive mechanism is introduced to estimate the related unknown bounds. Finally, the feasibility of the new RASMC strategy is illustrated by a numerical simulation.