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.
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Communicated by A. V. Balakrishnan
This research was supported by the Natural Sciences and Engineering Council Canada under grant A4641.
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Stern, R.J. A note on positively invariant cones. Appl Math Optim 9, 67–72 (1982). https://doi.org/10.1007/BF01460118
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DOI: https://doi.org/10.1007/BF01460118