Sliding Mode Controller Design for Switched Nonlinear Systems

This paper investigates the problem of sliding mode control (SMC) for discrete-time switched systems with repeated scalar nonlinearities. Firstly, a sufficient condition is presented to ensure the system considered to be exponentially stable with a prescribed weighed H-infinity gain performance. A novel switching surface function is designed by the average dwell time technique and the diagonally dominant Lyapunov function technique, thus to further reduce the conservativeness induced by the repeated scalar nonlinearity. Then the analysis of the sliding mode dynamics is made and the solvability condition for the desired switching surface function is derived. Furthermore, the synthesis of the proposed sliding mode control law is given to drive the system trajectories onto the predefined sliding surface in a finite time.