Volume no :9, Issue no: 2, May (2013)

Journal of Pure and Applied Mathematics: Advances and Applications

BARABANOV'S AUXILIARY SYSTEMS FOR A CLASS OF PERTURBED DIFFERENTIAL EQUATIONS

Author's: EFRÉN VÁZQUEZ SILVA and ROSA ISABEL URQUIZA SALGADO
Pages: [141] - [162]
Received Date: February 5, 2013
Submitted by:

Abstract

In this paper, we study the stability properties of the perturbed family when is a Hurwitz-stable matrix, are given matrices specifying the structure of the perturbation, represents the uncertainty of the perturbation; applying a theorem proved by Barabanov (see [1]). We obtain the explicit expressions for the so called auxiliary Barabanov’s systems. We also state a way in order to find the stability radius of the perturbed matrix A.

Keywords

perturbed systems of linear differential equations, asymptotic stability of the solutions, stability radius.