L₂-gain Analysis And Control Synthesis For A Class Of Uncertain Discrete-time Switched Nonlinear Systems

This paper is dedicated to the problem of L₂-gain and control synthesis for a class of uncertained switched systems in the discrete-time domain basing common Lyapunov function and switched Lyapunov function.L₂-gain analysis is used to characterize conditions under which an uncertain switched system satisfy the inner stability with an L₂-gain less than or equal to a constantγ.Control synthesis is to design switched-state feedback guaranteeing that the corresponding closed-loop system is asymptotically stable with an L₂-gain less than or equal to a constantγ.Applying the Lyapunov function theory and LMI,we give the sufficient conditions of the asymptotic stability for a class of uncertain discrete-time switched nonlinear system under arbitrary switching laws,whlie,we design the feedback control law such that the systems satisfy the inner stability.