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Related Experiment Video

Updated: Jun 5, 2025

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Synchronization of complex dynamical networks with saturated delayed impulsive control.

Zhilong He1, Chuandong Li2, Linfei Nie3

  • 1College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China; Institute of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, China.

ISA Transactions
|December 12, 2024
PubMed
Summary
This summary is machine-generated.

This study addresses complex dynamical networks synchronization using saturated delayed impulsive control. New methods ensure reliable synchronization despite system and coupling delays, enhancing network stability.

Keywords:
Complex dynamical networks (CDNs)Coupling delayLocal exponential synchronizationRazumikhin-type inequalityRegion of attraction (ROA)Saturated delayed impulsive control

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Area of Science:

  • Control Theory
  • Network Science
  • Dynamical Systems

Background:

  • Complex dynamical networks (CDNs) are crucial in various fields.
  • Synchronization in CDNs is vital for coordinated behavior.
  • Delays in systems and coupling can impede synchronization.

Purpose of the Study:

  • To investigate the local exponential synchronization of CDNs.
  • To address challenges posed by system and coupled delays.
  • To develop effective control strategies using saturated delayed impulsive control.

Main Methods:

  • Utilizing average impulsive interval (AII), average impulsive delay (AID), and average impulsive estimation (AIE).
  • Deriving a Razumikhin-type inequality for hybrid delayed impulses.
  • Applying Lyapunov stability theory and linear matrix inequalities (LMIs).

Main Results:

  • Sufficient synchronization criteria for local exponential synchronization are established.
  • Saturation nonlinearities are effectively handled using convex hulls.
  • A convex optimization problem is formulated to enhance control design.

Conclusions:

  • The proposed methods ensure effective local exponential synchronization for CDNs with delays.
  • The results provide a robust framework for designing controllers for complex networks.
  • Numerical examples validate the effectiveness of the developed criteria and methods.