Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints: L1- and Linfinity-gains characterization

TL;DR

This paper introduces a novel approach for analyzing and controlling uncertain linear positive systems using Integral Linear Constraints and linear supply-rates, enabling robust stability and performance assessment via linear programming.

Contribution

It develops a new framework combining copositive Lyapunov functions, dissipativity, and ILCs for robust stability and stabilization of uncertain positive systems, extending existing methods.

Findings

Robust stability conditions expressed as linear programs.

Extension to stabilization and performance optimization.

Finite-dimensional formulations via Handelman's Theorem.

Abstract

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for robustness and performance analysis using L1- and Linfinity-gains. Robust stability analysis is performed using Integral Linear Constraints (ILCs) for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's Theorem. Several examples are provided for illustration.