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This study is concerned with the problem of quasisliding mode control design for a class of discretetime systems with timevarying delay and unmatched disturbances. On the basis of the Lyapunovâ€“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 reducedorder system are exponentially convergent within a ball whose radius can be minimised to deal with the effects of timevarying delay and disturbances. A robust quasisliding 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.
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