New methods, for the design of different block diagrams of PLL, using the asymptotic analysis of high-frequency periodic oscillations, are suggested. The PLL description on three levels is made: 1)â€¦ (More)

An algorithm for searching hidden oscillations in dynamic systems is developed to help solve the Aizermanâ€™s, Kalmanâ€™s and Markus-Yamabeâ€™s conjectures well-known in control theory. The first step ofâ€¦ (More)

The method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden attractors of control systems. In the presentâ€¦ (More)

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (orâ€¦ (More)

New method for the rigorous mathematical analysis of electronic synchronization systems is suggested. This method allows to calculate the characteristics of phase detectors and carry out a rigorousâ€¦ (More)

Methods of harmonic linearization & describing function, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of periodic oscillations of controlâ€¦ (More)

New method for the rigorous mathematical nonlinear analysis of PLL systems is suggested. This method allows to calculate the characteristics of phase detectors and carry out a rigorous mathematicalâ€¦ (More)

The terms hold-in, pull-in (capture), and lock-in ranges are widely used by engineers for the concepts of frequency deviation ranges within which PLL-based circuits can achieve lock under variousâ€¦ (More)