Control of the new 4th order hyper-chaotic system with one input

Antonio Loria (1)

1 L2S - Laboratoire des signaux et systèmes

We solve the problem of chaos suppression of Lu's hyper-chaotic system via feedback control. We use only one control input and moreover the controller is a simple proportional feedback and uses the measurement of only one variable. We show that this simple control law suffices to stabilize the hyper-chaotic system to the zero equilibrium globally and asymptotically. We present stability proofs based on Lyapunov's direct method and integration of solutions. As a corollary of our main result we draw the conclusion that the system is globally stabilizable by simply varying one parameter, when possible. Simulation experiments that show the effectiveness of our method are also presented.

Mots clés: 05.45.Ac; 05.45.Gg; 02.30.Hq; 05.45.Pq

Domaines: Automatique / Robotique; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Antonio Loria. Control of the new 4th order hyper-chaotic system with one input. Communications in Nonlinear Science and Numerical Simulation, 2010, 15 (6), pp.1621-1630. ⟨10.1016/j.cnsns.2009.06.018⟩. ⟨hal-00521509⟩