On nonsingularity of a polytope of matrices. (English) Zbl 1152.15026
Given \(k\) real \(n\times n\) matrices \(A_1,\dots,A_k\), the authors study the nonsingularity and stability of the polytope \(\text{conv}\,\{A_1,\dots,A_k\}\) using the Bernstein algorithm of J. Garloff [Interval Comput. 1993, No. 2, 154–168 (1993; Zbl 0829.65017)] and of M. Zettler and J. Garloff [IEEE Trans. Autom. Control 43, No. 3, 425–431 (1998; Zbl 0906.93046)].
Reviewer: Martín Argerami (Regina)
MSC:
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 93D09 | Robust stability |
Keywords:
polytope of matrices; nonsingularity; stability; multivariate polynomial; Bernstein expansionReferences:
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