Structure of stability sets and asymptotic stability sets of families of linear differential systems with parameter multiplying the derivative: I

Author： Barabanov E.

Publisher： MAIK Nauka/Interperiodica

ISSN： 0012-2661

Source： Differential Equations, Vol.46, Iss.5, 2010-05, pp. : 613-627

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We consider families of linear differential systems continuously depending on a real parameter. The stability (respectively, asymptotic stability) set of such a family is defined as the set of all values of the parameter for which the corresponding systems in the family are stable (respectively, asymptotically stable). We show that a set on the real axis is the stability (respectively, asymptotic stability) set of some family of this kind if and only if it is an F _σ-set (respectively, an F _σδ-set). For families in which the parameter occurs only as a factor multiplying the matrix of the system, their stability sets are exactly F _σ-sets containing zero on the real line. The asymptotic stability sets of such families will be described in the second part of the present paper.