Robust discrete-time sliding mode control for multi-input uncertain time-delay systems

A robust discrete-time sliding mode control scheme is proposed for a class of linear multi-input uncertain systems with state delays. Systems are assumed to have structured mismatched time-varying parameter uncertainties and unknown bounded nonlinear function. A novel integral sliding surface is introduced to eliminate the reaching phase and a sliding mode controller is derived to ensure existence of the quasi-sliding mode. Based on an improved Lyapunov function and the linear matrix inequality technique, a sufficient condition for existence of a stable sliding surface is given and stability of the overall closed-loop system is guaranteed. The chattering phenomenon is eliminated and knowledge of the upper bound of external disturbances is not required. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme.