Justification of the Describing Function Method

摘要: Explicit conditions are given under which the use of describing function method to investigate nature oscillations in autonomous nonlinear feedback systems is justified. When these satisfied, bounds for frequency, fundamental magnitude, and higher harmonics oscillation based on approximation.The considered those can be decomposed into a linear time-invariant subsystem, not necessarily causal, stable, or finite-dimensional, frequency independent possibly containing hysteresis.The approach taken consider equation as an approximation determining periodic solutions system’s operator equation, local degree theory guarantee existence solution equation.