This work deals with the problem of absolute stability analysis for a class of uncertain Lur’e systems with time-varying delays. Novel delay-partitioning approaches are presented, which are dividing the variation interval of the delay into three subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on each of the obtained subintervals which can efficiently make use of the information of the delay and relate to the reciprocally convex combination technique and the Wirtinger-based integral inequality method. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). The merit of the proposed criteria lies in their less conservativeness and lower numerical complexity than relative literature. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.

这项工作解决了一类具有时变时滞的不确定Lur'e系统的绝对稳定性分析问题。提出了新颖的延迟划分方法，该方法将延迟的变化间隔分为三个子间隔。在每个获得的子区间上定义了一些新的增广Lyapunov–Krasovskii泛函（LKF），它们可以有效地利用时延信息，并且与倒凸组合技术和基于Wirtinger的积分不等式方法有关。根据线性矩阵不等式（LMI），得出了一些改进的依赖于延迟的标准。提出的标准的优点在于与相关文献相比，它们的保守性较低且数值复杂度较低。