Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 539056, 10 pages
Research Article

Chaotic Synchronization in a Small Network of a Class of Power Systems via Contraction Analysis

Departamento de Electrónica, CUCEI, Universidad de Guadalajara, Avenida Revolución No. 1500, 44430 Guadalajara, JAL, Mexico

Received 12 April 2012; Revised 7 June 2012; Accepted 8 June 2012

Academic Editor: Jun-Juh Yan

Copyright © 2012 G. Solís-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a synchronization analysis of networks of a class of power systems using the contraction theory for nonlinear systems. This analysis is characterized by not being based on Lyapunov's stability theory, that is, it is not required to determine a Lyapunov candidate function. Moreover, from the contraction conditions, robustness of the synchronization can be obtained, in this sense, the analysis method is robust. The analysis consists in identifying or proposing a virtual or auxiliary system which is contracting in a region of the state space. It is intended that in this region the trajectories of the systems on the network converge to those of the virtual system and then obtain the synchronization of the systems in the network. The contribution consists in applying this nontraditional analysis to the problem of chaotic synchronization of a network of a class of power systems.