Fixed-time stability of dynamical systems with impulsive effects

The present article is concerned with the fixed-time stability(FxTS) analysis of the nonlinear dynamical systems with impulsive effects. The novel criteria have been derived to achieve stability of the non-autonomous dynamical system in fixed-time under the effects of stabilizing and destabilizing impulses. The fixed time stability analysis due to the presence of destabilizing impulses in dynamical system, that leads to behavior of perturbing the systems' stability, have not been addressed much in the existing literature. Therefore, two theorems are constructed here, for stabilizing and destabilizing impulses separately, to estimate the fixed-time convergence precisely by using the concept of Lyapunov functional and average impulsive interval. The theoretical derivation shows that the estimated fixed-time in this study is less conservative and more accurate as compared to the existing FxTS theorems. Further, the theoretical results are applied to the impulsive control of general neural network systems. Finally, two numerical examples are given to validate the effectiveness of the theoretical results.(c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.