Sliding mode control for discrete-time descriptor Markovian jump systems with two Markov chains

This paper investigates sliding mode control problems for discrete-time descriptor Markovian jump systems which are supposed to contain two mutually independent homogeneous Markov chains. Firstly, the stochastic admissibility of the system with two Markov chains is analyzed and several necessary and sufficient conditions are obtained. A mode-independent sliding surface is then constructed, the stability of sliding mode dynamics is analyzed and the sliding mode controller is synthesized to ensure the finite-time reachability of the predefined sliding surface. Since the sliding surface is mode-independent, the effects of the switchings between two sequential subsystems on the convergence of the sliding surface are avoided. Finally, a numerical example is presented to illustrate the effectiveness of the developed theoretical results.