Hua, Changchun, Guan, Xinping and Shi, Peng (2004) Robust stabilization of a class of nonlinear time-delay systems. Applied Mathematics and Computation, 155 (3). pp. 737-752. ISSN 0096-3003

Abstract

The problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered. It is assumed that perturbations of the time-delayed sections are not bounded by first-order linear functions, but bounded by high-order functions with unknown gains. And the time delay considered is time varying. Two classes of controllers are proposed. When the time derivative of each time-varying time delay is less than 1, a class of adaptive state feedback controllers are proposed based on Lyapunov–Krasovskii method, which can render the closed-loop systems uniformly ultimately bounded stable. Novel nonlinear feedback controllers are developed by employing Razumikhin lemma, and the controller also can render the closed-loop systems stable in the sense of uniform ultimate boundedness. Finally, several examples are given to show the potential of the proposed techniques.

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