High-Order Polynomial Observer Design for Robust Adaptive Synchronization of Uncertain Fractional-Order Chaotic Systems

Abstract

Our focus in this paper is to present a new procedure of designing a high-order robust observer for chaos synchronization of a general class of uncertain nonlinear system with fractional-order derivative, using an adaptive strategy together with some parameter adjusting mechanisms. Some less stringent conditions for the exponential and asymptotic stability of adaptive robust control systems with fractional order are derived. A criterion for robust stability of an error system is obtained using the master–slave synchronization concept together with the Lyapunov stability theory associated with some algebraic manipulations. The high polynomial observer which can guarantee the robust stability of the closed loop system also rejects the effect of perturbations on the system dynamics within a prescribed level. The findings of this research are illustrated using computer simulations for the control problem of fractional Genesio–Tesi system. The proposed approach offers a systematic design procedure of a robust polynomial observer for the chaos synchronization of a large class of nonlinear systems.