基于时滞分割法的区间变时滞不确定系统鲁棒稳定新判据

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.

New robust stability criteria for uncertain systems with interval timevarying delay based on delay-partitioning approach

For a class of linear systems with norm-bounded uncertainty and interval time-varying delay, less conservative robust stability criteria is proposed based on the Lyapunov-Krasovskii(L-K) functional approach and linear matrix inequalitiy(LMI) technique. Firstly, the delay interval is partitioned into N equidistant subintervals and designing new L-K functional technique for each subinterval. Then, combined with a less conservative integral inequality, the time derivative of a candidate L-K functional is evaluated in each of these delay segments. Based on the convex combination technique, a new delay-dependent stability criteria for the system is formulated in terms of LMIs. Finally, numerical examples are given to show the effectiveness of the proposed approach.