多时变时滞系统的鲁棒稳定及有界实引理的时滞相关条件

Delay-dependent conditions for robust stability and bounded real lemma of systems with multiple time-varying delays

对于多时变时滞系统,引入表示牛顿-莱布尼兹公式中各项的相互关系的自由权矩阵,获得了基于线性矩阵不等式(LMI)描述的系统鲁棒稳定的时滞相关条件,并说明了时滞相关条件和时滞无关条件的相互关系.在此基础上,将其推广到有界实引理的时滞相关条件.所得结果克服了已有结果的保守性.最后给出实例说明本文方法的有效性.

Based on linear matrix inequality(LMI),some delay-dependent conditions were derived for the robust stability of the systems with multiple time-varying delays.Some free weighting matrices were employed to describe the reciprocal relationships between the terms in Newton-Leibniz formula.Then the relationship between the delay-dependent conditions and delay-independent ones were discussed.And,the results were extended to the delay-dependent bounded real lemma for systems.The proposed results overcome the conservativeness of the existing results.Finally,some examples were provided to demonstrate the (effectiveness) of the proposed method.