Sufficient condition for asymptotic stability of nonautonomous nonlinear-feedback systems by application of the modifed nonlinearity concept

The problem of deriving a sufficient condition for a given nonlinear system with a high-frequency input to be asymptotically stable is considered. It is suggested that the dynamics of the disturbed motion of the nonautonomous system can be approximated to sufficiently well by applying the concept of the so-called `modified nonlinearity¿. The system so obtained is in a form to which the theorem of Popov is applicable and provides a sufficient condition for the approximate nonautonomous system to be asymptotically stable. The results of this approach for systems with high-frequency sinusoidal and random input signals are examined. Some numerical examples are also presented to illustrate the simplicity of the method and also its usefulness.