Nonlinear Dynamics

, Volume 59, Issue 3, pp 485–496

Global asymptotical stability and generalized synchronization of phase synchronous dynamical networks

Original Paper

DOI: 10.1007/s11071-009-9555-3

Cite this article as:
Xu, S. & Yang, Y. Nonlinear Dyn (2010) 59: 485. doi:10.1007/s11071-009-9555-3


This paper examines the global asymptotical stability of the phase synchronous dynamical networks composed by a class of nonlinear pendulum-like systems with multiple equilibria. Sufficient conditions for the determination of global asymptotical stability are given in terms of linear matrix inequalities (LMIs). Furthermore, a concept of generalized synchronization is introduced, and the criterion of which is proposed in a simple form. Those results are of particular convenience for networks that possess large numbers of nodes, and they can be used to discuss controller design problems as well. Numerical simulations and analytical results are in excellent agreement with each other.


Dynamical networks Multiple equilibria Global asymptotical stability Phase synchronization LMI 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of EngineeringPeking UniversityBeijingPeople’s Republic of China

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