Previous published researches on chaos, controlling and synchronization in phasedlocked loops focused only on integer-order phase-locked loops. In this paper, we study control and synchronization of phase-locked loop systems based on fractional-order differential equations. Stability analyses of commensurate fractionalorder linear system are utilized to control chaotic behaviour exhibited by fractional-order differential equationbased phase-locked loop. Furthermore, chaos synchronization is obtained by employing the nonlinear state observer method. Finally, numerical simulations verify the effectiveness and applicability of our approaches.
Control and synchronization of fractional-order differential equations of phase-locked loop
Frasca M.;Caponetto R.;Fortuna L.
2012-01-01
Abstract
Previous published researches on chaos, controlling and synchronization in phasedlocked loops focused only on integer-order phase-locked loops. In this paper, we study control and synchronization of phase-locked loop systems based on fractional-order differential equations. Stability analyses of commensurate fractionalorder linear system are utilized to control chaotic behaviour exhibited by fractional-order differential equationbased phase-locked loop. Furthermore, chaos synchronization is obtained by employing the nonlinear state observer method. Finally, numerical simulations verify the effectiveness and applicability of our approaches.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.