Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer

This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics are considered as the master system and we propose the slave system structure which estimates the unknown state variables. Besides it is introduced a new fractional model free reduced order observer inspired on the new concept of Fractional algebraic observability (FAO); we applied the results to a Rössler hyperchaotic fractional order system and Lorenz fractional order system, and by means of some simulations we show the effectiveness of the suggested approach.