## 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.

### MSC:

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

### Keywords:

interval matrix; eigenvalue; stability; Gershgorin’s theorem
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