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

I. N Doye, K. N. Salama and T. Laleg-Kirati

IEEE/CAA Journal of Automatica Sinica, vol. 6, no. 1, pp. 268-277, January 2019.

Abstract: 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.