Cycle slipping in phase synchronization systems

Cycle slipping is a characteristically nonlinear phenomenon in phase synchronization systems, which is highly dependent of the initial state of the system. Slipping a cycle means that the phase error is increased to such an extent that the generator to be synchronized slips one complete cycle with respect to the input phase. In this Letter, a linear matrix inequality (LMI) based approach is proposed and the estimation of the number of cycles which slips a solution of the system is obtained by solving a quasi-convex optimization problem of LMI. Applications to phase locked loops demonstrate the validity of the proposed approach.