Synchronizing fractional order chaotic systems with an integer order observer

In this paper we present an observer based synchronization method to synchronize chaotic systems with unknown linearity and fractional order chaotic systems. Our method consists in designing a Luenberger like observer appended with an estimator of the unknown nonlinear function is slowly varying and that the observer converges quickly and uses the backward difference formula to approximate the state derivative. Next, our method is extended to synchronize fractional order chaotic systems. The efficiency of the proposed method is confirmed using numerical simulations.