A Combined Time-Frequency Condition for Stability of Time-Varying Systems With One Nonlinearity

Abstract

A means is presented for determining stability of linear time-varying systems with one feedback nonlinearity. The stability condition involves the minimization of certain time functions of the system coefficients as well as the imaginary axis behavior of a polynomial. It is required that the equation of the linear time-varying system be asymptotically stable and be in phase variable form. The nonlinearity is restricted to lie in a sector. For the limiting case of an autonomous linear system the criterion reduces to the Popov stability condition in certain cases.