Control and Synchronization of Fractional{Order Dierential Equations of Phase{Locked Loop

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 dierential equations. Stability analyses of commensurate fractional{ order linear system are utilized to control chaotic behaviour exhibited by fractional{ order dierential equation{based phase{locked loop. Furthermore, chaos synchroniza- tion is obtained by employing the nonlinear state observer method. Finally, numerical simulations verify the eectiveness