Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient

Abstract

This paper concerns sliding mode control problems for a class of descriptor Markovian jump systems with mode-dependent derivative-term coefficient. Firstly, a necessary and sufficient condition, under which such type descriptor Markovian jump systems with mode-dependent derivative-term coefficient are stochastically admissible, is proposed by means of the strictly linear matrix inequality (LMI) technique. Then a novel sliding surface function, in terms of both system states and inputs, is proposed for descriptor Markovian jump systems with mode-dependent derivative-term coefficient and a dynamic sliding mode controller is synthesized, which ensures the reachability of predefined sliding surface in finite time. It is also shown that the stochastic admissibility of the overall closed loop systems can be determined by checking the feasibility of a series of LMIs. Finally, an illustrative example on DC motor is provided to demonstrate the effectiveness of the theoretical results.