Elaboration of a generalized approach to control and to synchronize the fractional-order chaotic systems

In this paper, a new general optimal structure and parameters of the fractional-order feedback control law (OSP-FoF) is developed for controlling and synchronizing a large class of fractional-order chaotic systems (FoCS). The design of the OSP-FoF model is based on bounded-input bounded-output stabilization arguments, small gain theorem (SGT), and the matrix norms. The proposed model is theoretically rigorous and represents a powerful and simple approach which provides a reasonable trade-off between computational overhead, storage space, numerical accuracy and stability analysis for control and synchronization purposes of FoCS. Simulation results for the stabilization and synchronization of fractional-order hyperchaotic systems demonstrate the effectiveness of this newly proposed approach.