Circuit analysis using monotone+skew splitting

Thomas Chaffey, Sebastian Banert, Pontus Giselsson, Richard Pates

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–Vũ 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.