Chaos synchronization for a class of chaotic systems with model uncertainty and external disturbances

This paper proposes the generalized projective synchronization (GPS) for a class of nonlinear chaotic systems with model uncertainty and external disturbances via variable structure control. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic systems named as the master and the slave systems. The slave system is considered with model uncertainty and external disturbances. A sliding surface is adopted to ensure the stability of the error dynamics in variable structure control. The control law applied to chaos synchronization has been established in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the eigen values of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for GPS of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. Notice that it needs only one controller to realize GPS no matter how much dimensions the chaotic system contains and the controller is easy to be implemented. The designed controller is robust versus model uncertainty and external disturbances. The proposed method is applied to two chaotic systems; chaotic Gyroscope system and Genesio system. Numerical simulations are presented to verify the synchronization approach.