New Fixed-Time Stability Analysis of Delayed Discontinuous Systems via an Augmented Indefinite Lyapunov–Krasovskii Functional
研究了Filippov意义下一类时滞不连续系统的固定时间稳定性，通过增广不定Lyapunov-Krasovskii泛函给出新判据并估计了稳定时间，应用于时变时滞不连续惯性神经网络的控制。
This article discusses the fixed-time stability (FTS) of a kind of delayed discontinuous system (DS) in Filippov sense. Based on the set-valued map, the FTS analysis of the general solution is first transformed into the zero solution of the differential inclusion. Second, the new criteria of the Lyapunov-Krasovskii functional (LKF) are given and LKF is proved to possess the indefinite derivatives by using the simple integral inequalities. In addition, the FTS of the considered delayed DS is achieved and the new settling time is estimated. Third, to demonstrate the applicability of the new FTS theorems, the FTS control of a class of discontinuous inertial neural networks (DINNs) with time-varying delays is solved. Finally, two numerical examples are given to examine the theoretical results and simulations are also provided to make some illustrations.