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Research Article | Open Access

Note on prescribed-time stability of impulsive piecewise-smooth differential systems and application in networks

Chenchen Li1, Chunyan Zhang1, Lichao Feng1( ), Zhihui Wu2
College of Science, North China University of Science and Technology, Tangshan 063210, China
School of Automation, Harbin University of Science and Technology, Harbin 150080, China
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Abstract

We explored the prescribed-time stability (PTSt) of impulsive piecewise smooth differential systems (IPSDS) based on the Lyapunov theory and set-valued analysis technology, allowing flexibility in selecting the settling time as desired. Furthermore, by developing a feedback controller, we employed the theoretical results to evaluate the synchronization behavior of impulsive piecewise-smooth network systems (IPSNS) within a prescribed time frame and obtained novel criteria to guarantee the synchronization objective. A numerical example was presented to validate the accuracy of the results.

Keywords

feedback controllerimpulsive piecewise-smooth differential systemsprescribed-time stabilityprescribed-time synchronization

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Networks and Heterogeneous Media
Volume 19 Issue 3,
December 2024
Pages 970-991
DOI: 10.3934/nhm.2024043

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Cite this article:
Li C, Zhang C, Feng L, et al. Note on prescribed-time stability of impulsive piecewise-smooth differential systems and application in networks. Networks and Heterogeneous Media, 2024, 19(3): 970-991. https://doi.org/10.3934/nhm.2024043

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Received: 13 July 2024
Revised: 26 August 2024
Accepted: 13 September 2024
Published: 24 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)