Pattern Classification of Nonlinear Feedback Systems Using the Robust Perturbation Method

It is wellknown that the stability of nonlinear feedback systems depends considerably on their nonlinearities. The stability of a Lure-type nonlinear system with a pattern in which the nonlinearities lie on the first and third quadrants is studied. Identifying such patterns is important to enable system engineers to design stable nonlinear feedback systems. This paper presents a pattern classification method for systenms with arbitrary nonlinear feedback. Classification is carried out using the robust nonlinear-perturbation technique, in which nonlinearities are regarded as the nonlinear perturbations of linear stable systems. Stability theorems for the pattern classification of several types of nonlinear feedback are derived. In these theorems, the positive realness of the transfer function and the quadratic Lyapunov function are utilized.