Cycle slipping in discrete phase-controlled system

This paper considers cycle slipping of discrete phase-controlled system with periodic nonlinearity. The number of slipped cycles is an important characteristic of such nonlinear system. Based on Yakubovich-Kalman Lemma which establishes the equivalence between frequency domain inequalities (FDIs) and linear matrix inequalities (LMIs), the conditions of estimating the number of slipped cycles are derived. Then dynamic output feedback controller is designed to guarantee the nonexistence of cycle slipping. As a result, the transient performance of discrete phase-controlled system is improved. A concrete application to impulse phase-locked loop (PLL) shows the applicability and validity of the proposed approach.