Sliding mode control for a class of matched uncertain hybrid linear systems with Markovian jump parameter

The problem of sliding mode control for a class of uncertain hybrid linear systems with matched Markovian jump parameter is considered. Under the assumptions of matched known upper bound system uncertainties and unknown upper bound system uncertainties, the sufficient conditions are proposed to guarantee the mean exponentially stability of reduced-order sliding mode system. Under the assumption of two kinds of system uncertainties, conventional sliding mode control law and adaptive sliding mode control law are proposed. The control methods guarantee that the trajectory of system arrives at the sliding surface in finite time interval and is kept here thereafter. Finally, a simulation is given to illustrate the effectiveness of the proposed approach.