This paper considers the problem of passivity-based controller design for a new hyperchaotic system. By transforming this hyperchaotic system into an equivalent passive system, it is proved that the equivalent system can be asymptotically tracking the desired trajectories. The feasibility and effectiveness of the proposed scheme is demonstrated.

This paper investigates the control and the synchronization of a new 5D hyperchaotic system. Based on the impulsive control theory, some new and less conservative criteria for the global exponential stability and asymptotical stability of impulsively controlled 5D hyperchaotic system, are obtained with varying impulsive interval. Finally, numerical simulations are given to demonstrate the eectiveness of the proposed control and synchronization methodology.

This paper presents an interesting issue of using hybrid dynamical system to chaos synchronization and its application in secure communication using a new 5D hyperchaotic systems. The slave system is modeled by an unknown input observer, in which the unknown input issued from the hybrid system is the transmitted information. Based on the descriptor observer design, the Lyapunov stability theory and some robustness criteria, new sucient synthesis conditions are given in terms of linear matrix inequalities that we can obtain the estimations of both the hybrid system states and the transmitted signals. Numerical examples are provided to show the performances of the proposed approach.