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

Chenchen Li; Chunyan Zhang; Lichao Feng; Zhihui Wu; Chenchen Li; Chunyan Zhang; Lichao Feng; Zhihui Wu

doi:10.3934/nhm.2024043

Networks and Heterogeneous Media

2024, Volume 19, Issue 3: 970-991. doi: 10.3934/nhm.2024043

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Research article

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

1.
College of Science, North China University of Science and Technology, Tangshan 063210, China
2.
School of Automation, Harbin University of Science and Technology, Harbin 150080, China

Received: 13 July 2024 Revised: 26 August 2024 Accepted: 13 September 2024 Published: 24 September 2024

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.
- feedback controller,
- impulsive piecewise-smooth differential systems,
- prescribed-time stability,
- prescribed-time synchronization
Citation: Chenchen Li, Chunyan Zhang, Lichao Feng, Zhihui Wu. Note on prescribed-time stability of impulsive piecewise-smooth differential systems and application in networks[J]. Networks and Heterogeneous Media, 2024, 19(3): 970-991. doi: 10.3934/nhm.2024043

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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.

References

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