Functional Approximations of Various Characteristic Curves of Electronic Elements and Generalization of Equivalent Linearization and Describing Function Method

Abstract

Until today, equivalent linearization and describing function method have been known as a very powerfull tool for analyzing the nonlinear systems. However the application was restricted to only 2nd or 3rd ordersystem. In this paper, it was shown that Krylov-Bogoliubov method could be easily generalized to the nth order system using the polar-coordinates of n dimensional Euclidean R^n space, and equivalent linearization method was equivalent to take mean value in one functional space, For this analysis, the concepts of functional analysis, especially, the concept of L. Schwartz's distributions, Dirac's Dlta function δ(t), and the normed vector (functional) space etc., play important roles. Moreover, it will be shown that the knot theory on topology has some relation to the limit cycle of periodic solutions. This method and the concepts will be used for the nonlinear analysis in the near future.