Sufficient conditions on stability of interval matrices: Connections and new results. (English) Zbl 0752.15015

A quadratic real interval matrix \(A^ I\) is called stable with degree \(h\geq 0\) if \(\text{Re} \lambda<-h\) holds for any \(A\in A^ I\) and any eigenvalue \(\lambda\) of \(A\). If \(h=0\) then \(A^ I\) is called stable.
The paper presents several sufficient conditions for the stability behaviour of \(A^ I\). Their proofs are reduced to Gershgorin’s theorem and an extension of it. The conditions generalize a few criteria of other authors and the proofs help to find out some connections between these criteria.


15A42 Inequalities involving eigenvalues and eigenvectors
65G30 Interval and finite arithmetic
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