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

Content Provider	Springer Nature Link
Author	Barabav, E. A.
Copyright Year	2010
Abstract	We consider families of linear differential systems depending on a real parameter that occurs only as a factor multiplying the matrix of the system. The asymptotic stability set of such a family is defined as the set of all parameter values for which the corresponding systems in the family are asymptotically stable. We prove that a set on the real axis is the asymptotic stability set of such a family if and only if it is an F σδ-set lying entirely on an open ray with origin at zero. In addition, for any set of this kind, the coefficient matrix of a family whose asymptotic stability set coincides with this set can be chosen to be infinitely differentiable and uniformly bounded on the time half-line.
Starting Page	798
Ending Page	807
Page Count	10
File Format	PDF
ISSN	00122661
Journal	Differential Equations
Volume Number	46
Issue Number	6
e-ISSN	16083083
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2010-09-04
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Difference and Functional Equations Partial Differential Equations Ordinary Differential Equations
Content Type	Text
Resource Type	Article
Subject	Analysis

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