Stochastic sliding mode control for systems with Markovian jump parameters

in this paper, wo consider the problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps, in which the jumping parameters are modelled as a continuous-time, discrete-state homogeneous Markov process with right continuous trajectories taking values in a finite set. By using Linear matrix inequalities (LMI) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system and a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Simulation studies show the effectiveness of the control scheme.