A note on positively invariant cones
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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.
KeywordsDifferential Equation System Theory Mathematical Method Asymptotic Stability Linear Span
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