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Control and synchronization of fractional-order chaotic systems have attracted wide attention due to their numerous potential applications. To get suitable control method and parameters for fractional-order chaotic systems, the stability analysis of time-varying fractional-order systems should be discussed in the first place. Therefore, this paper analyzes the stability of the time-varying fractional-order systems and presents a stability theorem for the system with the order 0< α <1. This theorem is a sufficient condition which can discriminate the stability of time-varying systems conveniently. Feedback controllers are designed for control and synchronization of the fractional-order Lü chaotic system. The simulation results demonstrate the effectiveness of the proposed theorem.

Controlling and synchronizing a fractional-order chaotic system using stability theory of a time-varying fractional-order system