Discrete‐time sliding mode control with state bounding for linear systems with time‐varying delay and unmatched disturbances

This study is concerned with the problem of quasi‐sliding mode control design for a class of discrete‐time systems with time‐varying delay and unmatched disturbances. On the basis of the Lyapunov–Krasovskii method, combined with the reciprocally convex approach, sufficient conditions for the existence of a stable sliding surface are first derived in terms of matrix inequalities. These conditions also guarantee that the state trajectories of the reduced‐order system are exponentially convergent within a ball whose radius can be minimised to deal with the effects of time‐varying delay and disturbances. A robust quasi‐sliding mode control scheme is then developed to drive the system state trajectories towards that ball in a finite time and maintain them therein after subsequent time. A numerical example is given to illustrate the effectiveness of the proposed approach.