Fenchel duality of nonlinear networks

This paper contains an analysis of the interconnection of nonlinear -port networks. The primary goal of the paper is to extend to nonlinear networks the results derived previously for linear networks. The class of nonlinear networks considered have impedance functions that are subdifferentials of convex functions. Using the properties of the convex and impedance functions, it is shown that the network connections induce a natural operation on the class of impedance functions. The classical duality of current and voltage is expressed by using the concepts of conjugate functions, also known as Fenchel duality. Inequalities relating different network connections are also presented.