Stability Probability in Sliding Mode Control of Second Order Markovian Jump Systems

This paper explores the relationship between system stability conditional probability and the sliding mode control for second order continuous Markovian jump systems. By using the stochastic process theory, multi-step state transition conditional probability function is proposed for the continuous time discrete state Markovian process. A sliding mode control scheme is utilized to stabilize the continuous Markovian jump systems. The system stability conditional probability function is derived. It indicates that the system stability conditional probability is a monotonically bounded non-decreasing non-negative piecewise right continuous function of the control parameter. A numerical example is given to show the feasibility of the theoretical results.