Frequency estimates for the number of cycle slippings in a phase system with nonlinear vector function

Abstract

Two classes of phase control systems with vector nonlinearities are considered: systems described by ordinary differential equations and system described by difference equations. They are characterized by the presence of a periodic vector nonlinearity in the mathematical description of the system. The problem of the number of cycle slippings is investigated. For both classes of control systems, frequency estimates of the deviation of each angular coordinate from its initial value are obtained. The estimation technique is based on the direct Lyapunov method with periodic Lyapunov functions. With the use of the Yakubovich-Kalman lemma, all results are formulated in terms of the transfer function of the linear part of the system. The results obtained have the form of frequency inequalities with variable parameters, which satisfy some algebraic inequalities.