We consider a simple class of autonomous nonlinear systems, which includes several known chaotic and hyperchaotic dynamics. We first note that a system belonging to this class can be obtained from a linear system by means of a nonlinear state feedback. Then we show that a necessary condition for the existence of a nonlinear feedback generating chaotic dynamics is that the uncontrollable eigenvalues of the linear system, if any, must be stable. This result makes a contribution to the emerging issue of designing new chaotic systems. Finally, we give a unified framework to synchronize a class of autonomous as well as a class of nonautonomous chaotic or hyperchaotic systems via a scalar signal.
On a structural property for a class of chaotic systems / Mascolo, S.; Grassi, G.. - STAMPA. - (2001), pp. 1074-1078. (Intervento presentato al convegno 6th European Control Conference, ECC 2001 tenutosi a Porto, Portugal nel September 4-7 , 2001) [10.23919/ECC.2001.7076057].
On a structural property for a class of chaotic systems
Mascolo, S.;
2001-01-01
Abstract
We consider a simple class of autonomous nonlinear systems, which includes several known chaotic and hyperchaotic dynamics. We first note that a system belonging to this class can be obtained from a linear system by means of a nonlinear state feedback. Then we show that a necessary condition for the existence of a nonlinear feedback generating chaotic dynamics is that the uncontrollable eigenvalues of the linear system, if any, must be stable. This result makes a contribution to the emerging issue of designing new chaotic systems. Finally, we give a unified framework to synchronize a class of autonomous as well as a class of nonautonomous chaotic or hyperchaotic systems via a scalar signal.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
