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Applied Mathematics and Optimization

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

A note on positively invariant cones

  • Ronald J. Stern
Article

Abstract

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.

Keywords

Differential Equation System Theory Mathematical Method Asymptotic Stability Linear Span 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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