Delay-dependent robust stability for uncertain linear systems with interval time-varying delay.

*(English)*Zbl 1135.93024Summary: This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on the Lyapunov-Krasovskii functional approach, a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria. Numerical examples are given to demonstrate effectiveness of the proposed method.

##### MSC:

93D09 | Robust stability |

93C05 | Linear systems in control theory |

93C41 | Control/observation systems with incomplete information |

93D30 | Lyapunov and storage functions |

##### Keywords:

delay; stability; uncertainty; Lyapunov-Krasovskii functional; interval; linear matrix inequality
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\textit{X. Jiang} and \textit{Q.-L. Han}, Automatica 42, No. 6, 1059--1065 (2006; Zbl 1135.93024)

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