Fixed-time stability analysis of discontinuous impulsive systems

This article investigates the fixed-time stability (FXTS) of discontinuous impulsive systems. Based on the generalized Lyapunov functional (LF) method and some inequality techniques, we propose some novel FXTS criteria of the systems. It is worth mentioning that the derivative of LF can be negative...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2023-06, Vol.120, p.107153, Article 107153
Main Authors: Wang, Dongshu, Li, Luke
Format: Article
Language:English
Subjects:
Differential inclusions
Fixed-time stability
Impulsive system
Lyapunov method
Settling-time
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Summary:This article investigates the fixed-time stability (FXTS) of discontinuous impulsive systems. Based on the generalized Lyapunov functional (LF) method and some inequality techniques, we propose some novel FXTS criteria of the systems. It is worth mentioning that the derivative of LF can be negative definite or indefinite, and these results extend the previous results significantly. Furthermore, by using the monotonicity of the integral functions and the existence theorem of zero points, we obtain the FXTS results under the influence of impulses. In particular, when taking some certain functions, we can easily estimate the settling-time. Finally, the main results are confirmed by numerical simulations. •Fixed time stability is possible when the derivative of the Lyapunov function is indefinite.•Parameters of the inequality satisfied by Lyapunov function are relaxed to be time-varying functions.•Integrals of coefficient functions can be estimated with non-linear functions.•Settling time is irrelevant to the initial state values.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2023.107153