Computation of stability domains for uncertain systems with independent time delays

Abstract

In this paper, the stability of uncertain linear systems with time delay terms, described by quasipolynomials, is investigated. Two cases are studied: (i) system parameter perturbation and (ii) time delay perturbation, and the maximum allowable perturbations to maintain stability, are determined. For the first case, general lp-perturbations are considered and a simple numerical method is developed for the calculation of stability margins in the parameter space. For the second case, independent time delay perturbations are considered, and using the structure of the characteristic equations of time-delay systems, an algorithm is developed to calculate the stability domain, which requires searching the stability region contour and solving a system of equations. To illustrate the methods, various numerical examples are provided.