Applied Mathematics and Optimization

, Volume 9, Issue 1, pp 67–72 | Cite as

A note on positively invariant cones

  • Ronald J. Stern


Given a closed convex pointed cone
which is positively invariant with respect to motions of the differential equation\(\dot x = Ax\) (A being a real (n × n) matrix), it is proven that a necessary and sufficient condition for asymptotic stability of
(and therefore of the linear span of
) is
In case
, this result yields a known equivalence from the theory ofM-matrices.


Differential Equation System Theory Mathematical Method Asymptotic Stability Linear Span 
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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Ronald J. Stern
    • 1
  1. 1.Department of MathematicsConcordia UniversityMontrealCanada

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