Frequency-algebraic conditions for stability of phase systems with application to phase-locked loops and synchronization systems
Global asymptotic behavior of control systems with periodic vector nonlinearities and denumerable sets of equilibria is investigated. Multidimensional systems described by ordinary differential equations, distributed systems described by integrodifferential Volterra equations and discrete systems described by difference equations are examined. New kinds
of Lyapunov-type functions and Popov-type functionals are offered. New frequency-domain criteria for gradient-like behavior of the systems are obtained. They are applied to stability investigation of phase-locked loops and to the problem of self-synchronization of two rotors. CYBERNETICS AND PHYSICS, VOL. 1, No. 3, 2012 , 188–197.