Phase-locked loops redesign by the Lyapunov theory

A new approach is proposed to design a phase-locked loop (PLL) as an adaptive system in order to extract the desired sinusoidal component of the input signal, and estimate its amplitude and phase. In this method, the Lyapunov stability theorem is used to obtain adjustment rules for parameters, i.e. the stability of the system and convergence of the parameters are guaranteed in the sense of Lyapunov. Simulation results show the effectiveness of the proposed structure, and demonstrate that the input signal level and adaptation gains do not change the performance of the system. The proposed PLL structure can be utilised for fast and accurate applications in signal processing, power electronics, communication systems, and control.