Circuit Analysis using Monotone+Skew Splitting

TL;DR

This paper presents a novel approach to circuit analysis by representing circuit behavior as a zero of a sum of maximal monotone and skew-symmetric operators, enabling the use of the Condat-Vu algorithm for steady-state solutions.

Contribution

It introduces a new mathematical framework for circuit analysis combining monotone and skew operators, and applies the Condat-Vu algorithm to solve for steady states.

Findings

Framework effectively models circuit behavior with maximal monotone elements.

Algorithm computes periodic steady-state responses efficiently.

Method applicable to complex interconnection structures.

Abstract

It is shown that the behavior of an $m$-port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a structured skew-symmetric linear operator representing the interconnection structure, together with a linear output transformation. The Condat-V\~u algorithm solves inclusion problems of this form, and may be used to solve for the periodic steady-state behavior, given a periodic excitation at each port, using an iteration in the space of periodic trajectories.