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Sliding mode control for uncertain singular Markovian jump systems with actuator nonlinearities

This paper considers the design of the sliding mode control for uncertain singular Markovian jump systems with partially unknown transition rates and actuator nonlinearities. An integral sliding surface is designed, and the resulting sliding mode dynamics is the singular Markovian jump system. A set of sufficient conditions is proposed in terms of strict linear matrix inequalities to guarantee the stochastic admissibility of the sliding motion, from which all the parameter matrices in the integral sliding surface function can be calculated. Then, a sliding mode control law is synthesized such that the reachability condition is satisfied and thus the system is driven to the sliding surface in finite time and maintains a sliding motion on it thereafter. Finally, two examples are given to demonstrate the effectiveness of the results.