New results of stability analysis for systems with time-varying delay.

*(English)*Zbl 1185.93112Summary: This paper studies the problem of stability analysis for continuous-time systems with time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities. The merits of the proposed results lie in their less conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method.

##### MSC:

93D09 | Robust stability |

93C15 | Control/observation systems governed by ordinary differential equations |

34K35 | Control problems for functional-differential equations |

34D20 | Stability of solutions to ordinary differential equations |

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\textit{X.-L. Zhu} and \textit{G.-H. Yang}, Int. J. Robust Nonlinear Control 20, No. 5, 596--606 (2010; Zbl 1185.93112)

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