Robust sliding mode control for a class of uncertain hybrid linear systems with Markovian jump parameter

The robust sliding mode control problem of a class of uncertain hybrid linear systems with Markovian jump parameter is considered. Under the assumptions of unknown upper bounds matched system uncertainties and known upper bounds mismatched system uncertainties, the sufficient conditions are proposed to guarantee the mean exponentially stability of reduced-order sliding mode system. Under the conditions of two kinds of system uncertainties, adaptive robust sliding mode control law and general robust sliding mode control law are proposed. The control methods guarantees that the trajectory of system arrives at the sliding surface in finite time interval and is kept here thereafter. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of linear matrix inequalities(LMIs) have solution. Latsly a simulation is given to illustrate the effectiveness of the proposed approach.