Preservation of stability and synchronization of a class of fractional-order systems

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.