Chaos suppression in fractional systems using adaptive fractional state feedback control

This paper studies an adaptive Fractional Order (FO) state feedback control and the synchronization of FO chaotic systems. In the proposed algorithm, the feedback gain follows a FO adaptive control law. Two different control procedures are introduced namely full- and reduced-state feedback controllers, with single and vector variable feedback gains, respectively. The stability analysis is provided by means of the FO Lyapunov theorem both for the control and synchronization problems. Three examples are given to illustrate the effectiveness of the proposed scheme.