Synchronization and stabilization of fractional second-order nonlinear complex systems

Chaos control and synchronization of second- order nonautonomous fractional complex chaotic systems are discussed in this paper. A novel fractional nonsingular terminal sliding surface which is suitable for second-order fractional systems is proposed. It is proved that once the state trajectories of the system reach to the proposed sliding surface, they will be converged to the origin within a given finite time. After establishing the desired terminal sliding surface, a novel robust single sliding mode control law is introduced to force the system trajectories to reach the terminal sliding surface over a finite time. The stability and robustness of the proposed method are proved using the latest version of the fractional Lyapunov stability theorem. The proposed method is implemented for synchronization of two uncertain different fractional chaotic systems to confirm the theoretical results. Moreover, the fractional-order gyro system is stabilized using the proposed fractional sliding mode control scheme. It is worth noticing that the proposed fractional sliding mode approach is still a general control method and can be applied for control of second-order uncertain nonautonomous/autonomous fractional systems.