Intermittent and passivity based control strategies for a hyperchaotic system

In this paper a four-dimensional hyperchaotic system with only one equilibrium is consid-ered and it is shown how the control and the synchronization of this system can be realizedvia two different control techniques. Firstly, we propose a periodically intermittent con-troller to stabilize the system states to the equilibrium and to achieve the projective syn-chronization of the system both in its periodic and hyperchaotic regime. Then, based on thestability properties of a passive system, we design a linear passive controller, which onlyrequires the knowledge of the system output, to drive the system trajectories asymptoti-cally to the origin. Using the same passivity-based method, the complete synchronizationof the hyperchaotic system is also obtained. Both the intermittent and the passive control-lers are feedback, global and easy to implement. Numerical simulations are included toshow the effectiveness of the designed controllers in realizing the stabilization and the syn-chronization of the hyperchaotic system.