Sliding mode control for singular stochastic Markovian jump systems with uncertainties

This paper considers sliding mode control design for singular stochastic Markovian jump systems with uncertainties. A suitable integral sliding function is proposed and the resulting sliding mode dynamics is an uncertain singular stochastic Markovian jump system. A set of new sufficient conditions is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics, but is also constructive and determines all the parameter matrices in the integral sliding function. A set of new sufficient conditions is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics, but also determines all the parameter matrices in the integral sliding function. Then, a sliding mode control law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, three examples are given to demonstrate the effectiveness of the results.