Passivity-based chaos control and synchronization of a four-dimensional chaotic system

This paper addresses problems of chaos control and synchronization of a new four-dimensional (4D) chaotic system by applying the passive theory. With the study of the property of a passive system, the sufficient conditions were derived under which the controlled and error systems of the 4D chaotic system could be equivalent to passive systems. It can be proved that the new systems transformed by the controlled and error systems could be globally asymptotically stabilized at their equilibria, respectively, provided that suitable controllers were designed. Simulation examples are presented to illustrate the theoretical analysis.