In this paper, we consider nonlinear dynamics of a control circuit called phase-locked loop and provide a rigorous mathematical analysis to establish conditions under which the lock-in, pull-in, and hold-in ranges, which correspond to different types of system stability, coincide (the Viterbi problem). The analytical results are compared with both computer simulation and estimates of the lock-in and pull-in ranges, known from engineering literature. The comparison shows that those lock-in and pull-in range estimates may lead to cycle slipping and the loss of synchronization, respectively.
Original languageEnglish
Pages (from-to)13771–13789
JournalNonlinear Dynamics
Volume113
Issue number11
DOIs
StatePublished - 1 Jun 2025

    Research areas

  • Global stability, Hold-in range, Lock-in range, Lyapunov functions, Nonlinear analysis, Nonlinear control systems, PLL, Phase-locked loops, Pull-in range, Viterbi problem

ID: 134635821