On control for linear systems with interval time-varying delay |
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Authors: | Xiefu Qing-Long |
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Affiliation: | Faculty of Informatics and Communication, Central Queensland University, Rockhampton, QLD 4702, Australia |
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Abstract: | This paper deals with the problem of delay-dependent robust H∞ control for linear time-delay systems with norm-bounded, and possibly time-varying, uncertainty. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, and no restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. Based on an integral inequality, which is introduced in this paper, and Lyapunov–Krasovskii functional approach, a delay-dependent bounded real lemma (BRL) is first established without using model transformation and bounding techniques on the related cross product terms. Then employing the obtained BRL, a delay-dependent condition for the existence of a state feedback controller, which ensures asymptotic stability and a prescribed H∞ performance level of the closed-loop systems for all admissible uncertainties, is proposed in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the proposed method. |
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Keywords: | H∞ control Stability Bounded real lemma (BRL) Interval time-varying delay Linear matrix inequality |
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