Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach

Biwen Li; Qiaoping Huang; Biwen Li; Qiaoping Huang

doi:10.3934/mbe.2024199

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 4501-4520. doi: 10.3934/mbe.2024199

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Research article

Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach

Biwen Li ,
Qiaoping Huang ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Academic Editor: Xiangsheng Wang

Received: 20 December 2023 Revised: 04 February 2024 Accepted: 19 February 2024 Published: 28 February 2024

We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considered system. In addition, applying the proposed concepts of average positive impulsive estimation and average impulsive estimation, we integrated the information in impulsive delay into the rate coefficient to eliminate the limitation of having the same threshold at each impulse point, while the impulsive delay maintained the synchronization effect. This was an improvement on the previous results obtained. Finally, we provided two numerical examples to illustrate the validity of our results.
- impulsive delay,
- time-delay systems,
- synchronization,
- average impulsive estimation
Citation: Biwen Li, Qiaoping Huang. Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 4501-4520. doi: 10.3934/mbe.2024199

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Abstract

We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considered system. In addition, applying the proposed concepts of average positive impulsive estimation and average impulsive estimation, we integrated the information in impulsive delay into the rate coefficient to eliminate the limitation of having the same threshold at each impulse point, while the impulsive delay maintained the synchronization effect. This was an improvement on the previous results obtained. Finally, we provided two numerical examples to illustrate the validity of our results.

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