This paper addresses the design of a non-fragile exponential polynomial observer for a class of fractional-order nonlinear systems. Existence of the observer is proven and a sufficient condition for the stability of the state estimation error dynamics with a predetermined exponential convergence rate is derived employing the Lyapunov stability theorem. The exponential stability criterion is proposed in the form of linear matrix inequalities (LMIs). Moreover, some numerical examples have been provided to illustrate the effectiveness of the proposed approach. The synchronization of fractional-order Lorenz systems has been investigated using the proposed method. Then, the proposed method has been applied to the chaotic communication problem of fractional-order chaotic systems with four scroll attractors.
