Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 928930, 16 pages
Research Article

Preservation of Stability and Synchronization of a Class of Fractional-Order Systems

Departamento de Física y Matemáticas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, 01210 México, DF, Mexico

Received 18 April 2012; Revised 11 August 2012; Accepted 12 August 2012

Academic Editor: Ricardo Femat

Copyright © 2012 Armando Fabián Lugo-Peñaloza 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.


We present sufficient conditions for the preservation of stability of fractional-order systems, and then we use this result to preserve the synchronization, in a master-slave scheme, of fractional-order systems. The systems treated herein are autonomous fractional differential linear and nonlinear systems with commensurate orders lying between 0 and 2, where the nonlinear ones can be described as a linear part plus a nonlinear part. These results are based on stability properties for equilibria of fractional-order autonomous systems and some similar properties for the preservation of stability in integer order systems. Some simulation examples are presented only to show the effectiveness of the analytic result.