Discrete-time sliding mode control for state delay systems using nonlinear sliding surface

This paper considers the nonlinear surface design for uncertain discrete time system with state delay. Using Lyapunov-Krasovskii method delay-independent conditions are derived for the stable sliding motion along the nonlinear sliding surface. The sliding surface is typically designed to obtain the high speed response without exhibiting the overshoot. This can be achieved by keeping the damping ratio initially small and as the trajectory approaches to the origin, damping ratio is made high to avoid the overshoot in response.