Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

In this paper, we propose a robust fractional-order proportional-integral ( FOPI ) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities ( LMIs ) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional ( FOP ) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.