Monotone one-port circuits

TL;DR

This paper generalizes passivity using maximal monotonicity for one-port circuits, providing a new splitting algorithm for efficient input-output analysis of interconnected monotone elements.

Contribution

It introduces a maximal monotone framework for one-port circuits and develops a novel splitting algorithm for analyzing their input-output behavior.

Findings

Periodic signals are preserved through the circuits.

The splitting algorithm efficiently computes input-output behavior.

The framework generalizes passive LTI transfer functions.

Abstract

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series and parallel interconnection of basic elements. These circuits generalize passive LTI transfer functions. Periodic input signals are shown to be mapped to periodic output signals, and these input-output behaviors can be efficiently computed using a maximal monotone splitting algorithm, which decomposes the computation according to the circuit topology. A new splitting algorithm is presented, which applies to any monotone one-port circuit defined as a port interconnection of monotone elements.