Control and Synchronization of Fractional – Order Differential Equations of Phase – Locked Loop Viet –

Previous published researches on chaos, controlling and synchronization in phased–locked 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 fractional– order linear system are utilized to control chaotic behaviour exhibited by fractional– order differential equation–based 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.