Quasi-synchronization of nonlinear systems with parameter mismatch and time-varying delays via event-triggered impulsive control

Biwen Li; Yujie Liu; Biwen Li; Yujie Liu

doi:10.3934/math.2025174

AIMS Mathematics

2025, Volume 10, Issue 2: 3759-3778. doi: 10.3934/math.2025174

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Quasi-synchronization of nonlinear systems with parameter mismatch and time-varying delays via event-triggered impulsive control

Biwen Li ,
Yujie Liu ^,

Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 09 December 2024 Revised: 07 February 2025 Accepted: 18 February 2025 Published: 25 February 2025
MSC : 93C10, 93C65

This paper investigated the quasi-synchronization of nonlinear systems with parameter mismatch and time-varying delays via the event-triggered impulsive control (ETIC) approach, which integrates impulsive control and event-triggered control. The instances of impulsive activation were determined by an event-triggered mechanism based on a particular condition that depends on the system states. By employing the comparison principle for impulsive systems and the formula for variable parameters, we established the exact synchronization error bound and derived sufficient conditions for achieving quasi-synchronization. Furthermore, we proved the absence of Zeno behavior in the controlled system under the ETIC mechanism. Finally, we gave an example to verify that the theoretical results are valid under the proposed ETIC strategy.
- quasi-synchronization,
- event-triggered impulsive control,
- parameter mismatch,
- Zeno behavior,
- nonlinear systems,
- time-varying delays
Citation: Biwen Li, Yujie Liu. Quasi-synchronization of nonlinear systems with parameter mismatch and time-varying delays via event-triggered impulsive control[J]. AIMS Mathematics, 2025, 10(2): 3759-3778. doi: 10.3934/math.2025174

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Abstract

This paper investigated the quasi-synchronization of nonlinear systems with parameter mismatch and time-varying delays via the event-triggered impulsive control (ETIC) approach, which integrates impulsive control and event-triggered control. The instances of impulsive activation were determined by an event-triggered mechanism based on a particular condition that depends on the system states. By employing the comparison principle for impulsive systems and the formula for variable parameters, we established the exact synchronization error bound and derived sufficient conditions for achieving quasi-synchronization. Furthermore, we proved the absence of Zeno behavior in the controlled system under the ETIC mechanism. Finally, we gave an example to verify that the theoretical results are valid under the proposed ETIC strategy.

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