Dynamic feedback control for cycle slipping in a 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 the transient mode of such nonlinear systems. On the basis of the Yakubovich-Kalman lemma, linear matrix inequality (LMI) characterizations are derived for the number of slipped cycles of such systems and an efficient way of estimating the number is proposed by solving a generalized eigenvalue minimization problem. Furthermore, by 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 the phase-locked loop shows the applicability and validity of the proposed approach.