Robust stable, unstable and autooscillatory nonlinear systems under nonparametric uncertainty

A Lour´e-type nonlinear system with linear part nonparametric uncertainty is under the consideration. The circle criteria of robust stability, robust instability and robust auto-oscillating, ensuring those properties to remain for every system of a regarded family, are obtained. The family is defined by a maximal possible frequency response deviation from the nominal one and the nonlinear characteristics class. The circle criteria obtained are independent of the number of linear part right half-plane poles. The original absolute stability criterion as well as the robust stability criterion for linear systems are found to be the particular cases of the suggested one