Positive definiteness and stability of parametric interval matrices
Iwona Skalna
TL;DR
This paper studies conditions for positive definiteness and stability of parametric interval matrices, extending existing results and providing formulas for stability radius, with implications for systems with uncertain parameters.
Contribution
It introduces verifiable sufficient conditions for positive definiteness and stability of parametric interval matrices with non-linear and affine-linear dependencies, extending prior work.
Findings
Provides verifiable sufficient condition for positive definiteness.
Offers necessary and sufficient conditions for stability of symmetric matrices.
Derives a formula for the stability radius of symmetric parametric interval matrices.
Abstract
We investigate positive definiteness, Hurwitz stability and Schur stability of parametric interval matrices. We give a verifiable sufficient condition for positive definiteness of parametric interval matrices with non-linear dependencies. We also give several sufficient and necessary conditions for stability of symmetric parametric interval matrices with affine-linear dependencies. The presented results extend the results on positive definiteness and stability of interval matrices. In addition, we provide a formula for the radius of stability of symmetric parametric interval matrices.
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Taxonomy
TopicsNumerical Methods and Algorithms · Stability and Control of Uncertain Systems · Matrix Theory and Algorithms