Positive Definiteness and Stability of Interval Matrices

Authors:
Jiri Rohn
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1994

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Abstract

Characterizations of positive definiteness, positive semidefiniteness, and Hurwitz and Schur stability of interval matrices are given. First it is shown that an interval matrix has some of the four properties if and only if this is true for a finite subset of explicitly described matrices, and some previous results of this type are improved. Second it is proved that a symmetric interval matrix is positive definite (Hurwitz stable, Schur stable) if and only if it contains at least one symmetric matrix with the respective property and is nonsingular (for Schur stability, two interval matrices are to be nonsingular). As a consequence, verifiable sufficient conditions are obtained for positive definiteness and Hurwitz and Schur stability of symmetric interval matrices.