Year: 2023
Author: Guihua Zhao, Hui Liang
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 49–68
Abstract
In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented. 2) When the system without impulsive effects is globally finite-time stable (GFTS) and the settling time is continuous at the origin, it is proved that it is still GFTS over any class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions. 3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the destabilizing impulses should not occur too frequently, otherwise, the origin of the impulsive system is finite-time instable, which are formulated by average dwell time (ADT) conditions respectively. 4) A theorem on finite-time instability is provided for system with stabilizing impulses. For each GFTS theorem of impulsive systems considered in this paper, the upper boundedness of settling time is given, which depends on the initial value and impulsive effects. Some numerical examples are given to illustrate the theoretical analysis.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0381
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 49–68
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Impulsive systems finite-time stability finite-time instability nonlinear systems.
Author Details
-
Existence of weak solutions for stochastic nonlinear impulsive systems
Zhao, Gui-Hua
Systems & Control Letters, Vol. 182 (2023), Iss. P.105660
https://doi.org/10.1016/j.sysconle.2023.105660 [Citations: 0] -
Instability of dynamical systems subjected to impulsive actions.
Dashkovskiy, Sergey | Slynko, Vitalii2023 European Control Conference (ECC), (2023), P.1
https://doi.org/10.23919/ECC57647.2023.10178120 [Citations: 0]