Impulsive synchronization of fractional order hyperchaotic systems based on comparison system

In this paper, a novel impulsive control method based on comparison system is proposed to realize complete synchronization of a class of fractional order chaotic systems. By constructing the suitable response system, the original fractional order error system can be converted into the integral order one. Based on the theory of Lyapunov stability and impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Compared with the existing results, the main results in this paper are more practical and rigorous. Simulation results for fractional order Chen system show the effectiveness and the feasibility of the proposed impulsive control method.