Elsevier

Automatica

Volume 35, Issue 7, July 1999, Pages 1313-1321
Automatica

Brief Paper
Delay-dependent robust H control of uncertain linear state-delayed systems

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Abstract

This paper examines the problems of robust stabilization and robust H control for linear systems with a constant time delay in the state and subject to parameter uncertainty. Systems with norm-bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers. We develop methods of robust stabilization and robust H control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities. The proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays.

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    Different approaches are presented in the literature to compute the stability radius for a class of linear delay systems affected by such uncertainties, and we refer to the monographs [1–3]. The Lyapunov-based approach allows for a broad class of uncertainties, such as time-varying perturbations [4,5] and perturbations on delay values [6]. However, these methods are based on sufficient conditions for stability, which typically lead to conservative lower bounds on the stability radius.

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A preliminary version of this paper was presented at the 13th IFAC World Congress, which was held in San Francisco, USA during June 30–July 5, 1996. This paper was recommended for publication in revised form by Associate Editor Y. Yamamoto under the direction of Editor R. Tempo.

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