CIRCLE CRITERIA IN RECURSIVE-IDENTIFICATION

Positive real conditions and differential sector conditions have recen tly been shown to imply global convergence w.p. 1, for recursive ident ification schemes based on a class of single-input/single-output nonli near Wiener models. The models consist of linear dynamics followed by a static output nonlinearity. The model structure is hence closely rel ated to that of the Lure problem in the stability theory of feedback s ystems. This paper proves that the conditions for convergence can be t ransformed to graphical circle criteria, depending on the sector condi tions and on the Nyquist plot of a transfer function related to the pr ior knowledge of the poles of the identified system.