Non-linear stability analysis for restricted non-linearities using the second method of liapunov

Abstract

The methods treating the stability of a closed loop with single nonlinearity lead to stability conditions that assure stability regardless of the shape of the non-linearity within a section in the non-linear plane. Thus, the stability criteria are always more than sufficient conditions for non-linearities that accept some restrictions on its shape. These restrictions must cause relaxation of the stability conditions. In this paper, this approach is used for both inherently stable and unstable control systems to get stability criteria that take into consideration the restrictions on the shape of the non-linearity.