Intermittent and passivity based control strategies for a hyperchaotic system

In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and it is shown how the control and the synchronization of this system can be realized via two different control techniques. Firstly, we propose a periodically intermittent controller to stabilize the system states to the equilibrium and to achieve the projective synchronization of the system both in its periodic and hyperchaotic regime. Then, based on the stability properties of a passive system, we design a linear passive controller, which only requires the knowledge of the system output, to drive the system trajectories asymptotically to the origin. Using the same passivity-based method, the complete synchronization of the hyperchaotic system is also obtained. Both the intermittent and the passive controllers are feedback, global and easy to implement. Numerical simulations are included to show the effectiveness of the designed controllers in realizing the stabilization and the synchronization of the hyperchaotic system.