Cycle Slipping Phenomenon in Synchronous Control Systems

Cycle slipping is a characteristically nonlinear phenomenon in synchronous control systems. 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 paper, linear matrix inequality (LMI) conditions for the existence of cycle slipping in a synchronous control system 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.