This paper concentrates on the stability analysis of continuous-time linear systems with multiple time-varying delays. The time-delays are assumed to be bounded and have or not lower and upper bounds on their time-derivative. Based on the Lyapunov-Krasovskii theory the proposed results formulated as linear matrix inequality conditions can verify the delay-intervals for which the system stability is preserved. The main results follow from developing new augmented Lyapunov-Krasovskii functionals that exploit the benefits of the Bessel-Legendre-based integral inequality and the reciprocally convex approach. Also, the proposed functionals allow us to take advantage of the relationships between the current and delayed states. As a result, the proposed stability conditions outperformed similar existing ones in all numerical tests accomplished in this paper.

本文主要研究具有多个时变时滞的连续时间线性系统的稳定性分析。假设时间延迟是有界的，并且它们的时间导数有或没有下限和上限。基于 Lyapunov-Krasovskii 理论，提出的结果表述为线性矩阵不等式条件可以验证延迟间隔，从而保持系统稳定性。主要结果来自开发新的增强 Lyapunov-Krasovskii 泛函，这些泛函利用了基于 Bessel-Legendre 的积分不等式和互反凸方法的优点。此外，提议的泛函允许我们利用当前状态和延迟状态之间的关系。其结果，