This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

中文翻译：

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具有时变延迟和扇区有界非线性的 Lur'e 系统的新鲁棒稳定性准则

本文处理具有时变延迟和扇区有界非线性的不确定 Lur'e 系统的鲁棒稳定性问题。通过改进的 Lyapunov-Krasovskii 泛函 (LKF) 方法提出了改进的依赖于延迟的鲁棒稳定性准则。首先构造了一个由时滞相关矩阵和两个时滞子区间下的双积分项组成的修正LKF，从而充分利用时滞及其导数信息。其次，通过二次函数应用的性质，稳定性准则可以表示为凸线性矩阵不等式（LMI）。第三，为了进一步降低稳定性标准的保守性，使用二次广义自由加权矩阵不等式（QGFMI）。最后，一些数值例子，