A Lyapunov-Based Distri buted Framework for Complete and Phase Synchronization in Chaotic Multi-Agent Systems

TL;DR

This paper introduces a distributed Lyapunov-based control method for achieving complete and phase synchronization in chaotic multi-agent systems, using nonlinear coupling and stability theory to ensure robust convergence with limited information.

Contribution

It proposes a novel nonlinear coupling mechanism and a Lyapunov-based framework that simplifies synchronization conditions compared to traditional methods.

Findings

Successful synchronization of Roessler, Lu, and Chen systems.

Enhanced convergence rate and robustness demonstrated.

Reduced computational complexity compared to existing approaches.

Abstract

This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach introduces a novel nonlinear coupling mechanism and utilizes Lyapunov stability theory combined with matrix measure analysis to derive explicit synchronization conditions. In contrast to traditional LMI-based or adaptive methods, the present approach guarantees synchronization under limited topological information and reduced computational complexity. Three classical chaotic systems - Roessler, Lu, and Chen - are used to validate the theoretical results, confirming the superior convergence rate and robustness of the proposed scheme.