Sliding mode control for mismatched uncertain Markov jump systems

The sliding mode control problem of a class of mismatched uncertain Markov jump systems is considered. On the assumption that the system uncertainties are known upper bounds, the sufficient conditions are proposed respectively via linear matrix inequalities to guarantee the mean exponential stability of reduced-order sliding mode system. Corresponding to mismatched system uncertainties, a robust sliding mode controller is designed, which is proved able to guarantee that the system trajectory reach the sliding surface in a finite time interval and keep up here thereafter. Simulation results demonstrate that the proposed controller has good stability and robustness for uncertain hybrid linear Markov jumping systems.