Control and synchronization of fractional-order differential equations of phase-locked loop

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.