Bounded synchronization of fractional-order chaotic systems with external disturbance based on dissipative decomposition

Abstract Compared with the classical synchronization phenomena, practical synchronization considers the factors of the real environment and has a wider range of applications. For fractional- order disturbed systems, a practical synchronization type, bounded synchronization, is discussed for the first time. The proposed synchronization model does not require the error system to converge completely to the origin but allows convergence to a bounded region around the origin. Employing the dissipative decomposition of vector field, a simple and novel synchronization scheme is presented for a class of fractional-order chaotic systems with external disturbance. The Mittag-Leffler input stability of the error system can be guaranteed by means of fractional-order stability theory. Two fractional-order chaotic systems with periodic and noise disturbances, respectively, are taken as examples to demonstrate the feasibility of the proposed method. Numerical results indicate that regardless of the disturbance, the error system is eventually kept within the boundary and the boundary values are related to the controller strength. Furthermore, the effect of controller parameters on the error boundary is also analyzed, and the results help to select the control parameters according to the actual needs in the application.