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Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay
This study addresses complex network synchronization with nondifferentiable time-varying delays using adaptive control. We establish new synchronization criteria, overcoming previous limitations in network control theory.
Area of Science:
- Control Theory
- Network Science
- Applied Mathematics
Background:
- Complex networks are crucial in various fields, but their synchronization analysis is often limited by assumptions of differentiable time delays.
- Nondifferentiable time-varying delays present significant challenges in achieving network synchronization via adaptive control.
Purpose of the Study:
- To investigate and establish synchronization criteria for complex networks with general, including nondifferentiable, time-varying delays.
- To overcome the limitations of existing methods that assume differentiable delays.
Main Methods:
- Analysis of the boundedness of adaptive control gain.
- Extension of the Halanay inequality to handle nondifferentiable delays.
- Development of centralized and decentralized adaptive control strategies.
Main Results:
- Synchronization criteria are established for complex networks with nondifferentiable time-varying delays.
- The boundedness of the centralized adaptive control gain is theoretically proven.
- Numerical simulations validate the derived synchronization criteria.
Conclusions:
- The proposed adaptive control methods effectively achieve synchronization in complex networks with challenging nondifferentiable time-varying delays.
- This work advances the understanding and practical application of control strategies for complex network synchronization.
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