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

Abstract

The robust sliding mode control problem of a class of uncertain hybrid linear systems with Markovian jump parameters is considered. Under the assumption of unknown upper bounds matched system uncertainties, the sufficient conditions are proposed to guarantee exponentially stable in mean square of reduced-order sliding mode system. Under the conditions of unknown upper bounds of system uncertainties, adaptive robust sliding mode control law is 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.