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Necessary and sufficient conditions for stability of a class of interval matrices. (English) Zbl 0611.15017
A $n\times n$ interval matrix $A\sp I=([p\sb{ij},q\sb{ij}])\sb{i,j=1,...,n}$ is said to be stable [completely unstable] if all point matrices $A\in A\sp I$ are stable [unstable]. If $A\sp I$ contains both, stable as well as unstable point matrices then $A\sp I$ is called of composite stability type. In the first of the two papers, conditions are established that are sufficient for $A\sp I$ to be stable, to be unstable, and to be of composite type. - The second paper is concerned with that special class of interval matrices $A\sp I$ which satisfy $q\sb{ii}<0$ $(i=1,...,n)$ and $p\sb{ij}\ge 0$ $(i,j=1,...,n$; $i\ne j)$. For this special class, necessary and sufficient conditions for $A\sp I$ to be stable, to be unstable or to be of composite type are given.
Reviewer: H.Ratschek

15B57Hermitian, skew-Hermitian, and related matrices
15A42Inequalities involving eigenvalues and eigenvectors
65G30Interval and finite arithmetic
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