Output feedback controller for cycle slipping in phase-controlled system

This paper concerns the problem of cycle slipping for continuous phase-controlled systems with periodic nonlinearity. The number of slipped cycles is an important property in transient mode of such nonlinear systems. Based on Yakubovich-Kalman Lemma, LMI characterizations are derived for the number of slipped cycles of such systems and an efficient way for the estimation of the number is proposed by solving a generalized eigenvalue minimization problem. Furthermore, in virtue of these results, a dynamic output feedback controller is designed to guarantee the nonexistence of cycle slipping. As a result, the transient performance of phase- controlled system is improved. A concrete application to phase- locked loop (PLL) shows the applicability and validity of the proposed approach.