Sliding-Mode Variable Structure Control for Markov Jumping Uncertain Systems with Time-Varying Delay

For a class of Markov jumping uncertain systems with time-varying delay, the sliding-mode variable structure control algorithm is designed based on sliding mode control theory. By studying nonsingular transform of the system, a sufficient condition for the existence of stochastic stable sliding surfaces is established in terms of linear matrix inequalities (LMIs). On the basis of this existence condition, the synthesized variable structure control strategy is designed via exponential approach law, which is proved to guarantee that the system trajectory reaches the sliding surface in a finite time interval and keeps up here thereafter. Finally, an illustrative example demonstrates the correctness and feasibility of the proposed approach.