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Robust stabilisation of uncertain systems with interval time-varying state and input delays

This article is concerned with robust stabilisation of uncertain systems with interval time-varying state and input delays. The system uncertainties under consideration are unknown and time-varying, but norm-bounded. The time delays vary in intervals. A robust stabilisation condition and the corresponding controller are constructed by solving two linear matrix inequalities. The auxiliary variables and generalised state methods are used to prove the asymptotic stability of the closed-loop system. In the proposed control design, there are no restrictions on the derivatives of the time delays, allowing fast time-varying delays. Examples and simulation results have confirmed the effectiveness and superiority of the proposed method.