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针对一类存在泛数有界不确性的区间变时滞线性系统,利用Lyapunov-Krasovskii(L-K)泛函方法并结合线性矩阵不等式(LMI)技术建立一种新的保守性更低的鲁棒稳定性判据.首先基于时滞分割方法将时滞区间均分成N等分,针对不同的子区间构造合适的L-K泛函;然后在各自的分割区间采用保守性较小的积分不等式处理泛函沿时间的导数,基于凸组合技术建立了LMI形式的时滞相关稳定性新判据;最后通过数值实例验证了结论的有效性.
For a class of linear systems with interval varying delay with generalized bounded uncertainties, a new conservative lower robustness is established by Lyapunov-Krasovskii (LK) functional approach combined with linear matrix inequality (LMI) Stability criterion.Firstly, based on the method of time-delay partitioning, the time-delay interval is divided into N equally, and the appropriate LK functional is constructed for different sub-intervals. Then, the functional LKM with less conservative integral inequalities Based on the derivative of time, a new criterion of LMI-type delay-dependent stability is established based on the convex combination technique. Finally, the numerical example is used to verify the validity of the conclusion.