Robust stability analysis for systems with real parametric uncertainty: Implementation of graphical tests in Matlab

Abstract

This paper is focused mainly on demonstration of simple Matlab programs suitable for plotting the value sets of systems with real parametric uncertainty represented by families of polynomials. The behaviour of obtained value sets and especially their position in relation to the origin of the complex plane is convenient criterion of robust stability/instability. The paper presents number of illustrative examples for various simple as well as complicated structures of uncertainty mainly for continuous-time families including the Matlab codes and robust stability analyses. On top of that, the work covers also cases of a quasi-polynomial or discrete-time interval polynomial.