Stability Analysis of Linear Uncertain Systems via Checking Positivity of Forms on Simplices

TL;DR

This paper introduces a finite-step method to verify the robust Hurwitz stability of linear systems with matrix entries as rational functions of uncertain parameters, enhancing stability analysis under broader uncertainties.

Contribution

The paper proposes a novel finite-step approach for stability verification of systems with rational function uncertainties, extending existing methods.

Findings

Method efficiently checks stability in finite steps

Examples demonstrate the approach's effectiveness

Applicable to systems with interval-varying parameters

Abstract

In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions of uncertain parameters which are varying in intervals. we present a method which can check the robust Hurwitz stability of such uncertain systems in finite steps. Examples show the efficiency of our approach.