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**On \(H_{\infty}\) control for linear systems with interval time-varying delay.**
*(English)*
Zbl 1100.93017

Summary: This paper deals with the problem of delay-dependent robust \(H_{\infty}\) 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 \(H_{\infty}\) 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.

### MSC:

93B36 | \(H^\infty\)-control |

93C23 | Control/observation systems governed by functional-differential equations |

93D15 | Stabilization of systems by feedback |

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\textit{X. Jiang} and \textit{Q.-L. Han}, Automatica 41, No. 12, 2099--2106 (2005; Zbl 1100.93017)

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### References:

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