A new discrete-time integral sliding mode control scheme is proposed for a class of linear multi-input systems with state delays. Based on the Lyapunov stability theory and one-step delayed disturbance approximation, a sliding mode controller not only drives the sliding mode into the O(T2 ) boundary, but also achieves the O(T2 ) boundary for state regulation. A novel integral sliding surface is introduced so that reaching phase is eliminated. Chattering phenomenon is eliminated and the knowledge of upper bound of external disturbances is not required. The validity of the proposed control methodology is demonstrated by simulation results.

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