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Impulsive strategies in nonlinear dynamical systems: A brief overview.
Haitao Zhu1, Xinrui Ji1,2, Jianquan Lu1
1Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China.
Mathematical Biosciences and Engineering : MBE
|March 11, 2023
Summary
This review explores impulsive dynamical systems, focusing on time delays, event-based control, and hybrid effects in nonlinear systems. It highlights applications in network synchronization and presents key stability results.
Area of Science:
- Dynamical Systems and Control Theory
- Nonlinear Dynamics
- Network Science
Background:
- Impulsive dynamical systems are well-researched, with numerous publications available.
- This study focuses on continuous-time systems and reviews various impulsive strategies.
Purpose of the Study:
- To provide an exhaustive review of different impulsive strategies in continuous-time systems.
- To emphasize the impact of time delays and event-based mechanisms on system stability.
- To investigate hybrid impulse effects and applications in network synchronization.
Main Methods:
- Review of existing literature on impulsive dynamical systems.
- Analysis of impulse-delay structures and their effect on stability.
- Systematic introduction of event-based impulsive control strategies.
- Investigation of hybrid impulse effects in nonlinear systems and network synchronization.
Main Results:
- Discussion of two impulse-delay structures and their stability implications.
- Introduction of novel event-triggered mechanisms for impulse control.
- Revelation of constraint relationships between different impulses in nonlinear systems.
- Exploration of recent applications in the synchronization of dynamical networks.
Conclusions:
- Significant stability results for impulsive dynamical systems have been presented.
- The review provides a detailed introduction to the field.
- Future research challenges in impulsive dynamical systems are identified.
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