Positive Systems Analysis Via Integral Linear Constraints

TL;DR

This paper investigates the positivity of feedback interconnections in positive monotone systems, introducing integral linear constraints (ILC) as a tool for robustness analysis of uncertain positive feedback systems.

Contribution

It establishes conditions linking gain and positivity, and applies ILC to analyze robustness in positive linear and nonlinear systems, extending existing quadratic constraint methods.

Findings

Instantaneous gain condition guarantees feedback positivity.

ILC effectively characterizes uncertainty in positive feedback systems.

Robustness of positive LTV and nonlinear systems is analyzed using ILC.

Abstract

Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees feedback positivity. Furthermore, the notion of integral linear constraints (ILC) is utilised as a tool to characterise uncertainty in positive feedback systems. Robustness analysis of positive linear time-varying and nonlinear feedback systems is studied using ILC, paralleling the well-known results based on integral quadratic constraints.