The delays-dependent stability analysis of linear systems with multiple time-varying delays is addressed in this study. To estimate the integral term that results from the differentiation of Lyapunov–Krasovskii functional (LKF), an improved region partitioning approach and relaxed lemmas are proposed. Based on all the delayed state information, the maximum delay interval is separated into non-overlapping subintervals. Secondly, two novel generalized reciprocally convex combination lemmas (GRCCLs) are proposed, with Bessel–Legendre-based inequality, to estimate the integral terms generated by the region partitioning approach to obtain less conservative stability criteria. Finally, the obtained stability criteria is applied to simple linear systems and load frequency control (LFC) scheme of the two-area power system for stability analysis, and the effectiveness of proposed method is verified.

中文翻译：

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通过区域划分方法和互凸组合引理对具有多个时变延迟的线性系统进行稳定性分析


本研究解决了具有多个时变延迟的线性系统的延迟相关稳定性分析。为了估计 Lyapunov-Krasovskii 泛函 (LKF) 微分所产生的积分项，提出了一种改进的区域划分方法和松弛引理。基于所有延迟状态信息，最大延迟间隔被分成不重叠的子间隔。其次，提出了两种新颖的广义互凸组合引理（GRCCL），以及基于贝塞尔-勒让德的不等式，来估计区域划分方法生成的积分项，以获得不太保守的稳定性标准。最后，将得到的稳定性判据应用于简单线性系统和两区域电力系统的负载频率控制（LFC）方案进行稳定性分析，验证了所提方法的有效性。