Canonical Construction of Polytope Barabanov Norms and Antinorms for Sets of Matrices

DOI10.1137/140962814zbMath1320.15017OpenAlexW1483207600MaRDI QIDQ5254398

Marino Zennaro, Nicola Guglielmi

Publication date: 9 June 2015

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f4ac8509ca71323c7548123e6c04c0b2e663561c

zbMATH Keywords

joint spectral radiuslower spectral radiusinvariant normunit antiballpolytope Barabanov antinormpolytope barabanov normpolytope extremal antinormpolytope extremal norm

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Software, source code, etc. for problems pertaining to linear algebra (15-04)

Related Items (12)

Linear switched dynamical systems on graphs ⋮ The Barabanov Norm is Generically Unique, Simple, and Easily Computed ⋮ Antinorms on cones: duality and applications ⋮ Antinorms and self-polar polyhedra ⋮ Resonance and marginal instability of switching systems ⋮ Elliptic polytopes and invariant norms of linear operators ⋮ Spectrum Maximizing Products Are Not Generically Unique ⋮ An Irreducible Linear Switching System Whose Unique Barabanov Norm Is Not Strictly Convex ⋮ An antinorm theory for sets of matrices: bounds and approximations to the lower spectral radius ⋮ Invariant multicones for families of matrices ⋮ Subspace confinement for switched linear systems ⋮ Comprehensive Lyapunov functions for linear switching systems

Cites Work

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• Invariant functionals for random matrices
• Explicit construction of a Barabanov norm for a class of positive planar discrete-time linear switched systems
• Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets
• Finiteness property of pairs of \(2\times 2\) sign-matrices via real extremal polytope norms
• Lyapunov indicator of discrete inclusions. I
• Bounded semigroups of matrices
• Gian-Carlo Rota on analysis and probability. Selected papers and commentaries. Edited by Jean Dhombres, Joseph P. S. Kung and Norton Starr
• The generalized spectral-radius theorem: An analytic-geometric proof
• Computing the joint spectral radius
• Exact computation of joint spectral characteristics of linear operators
• On the finiteness property for rational matrices
• Duality results for the joint spectral radius and transient behavior
• A New Sufficient Condition for the Uniqueness of Barabanov Norms
• A relaxation scheme for computation of the joint spectral radius of matrix sets
• Orthonormal bases of compactly supported wavelets
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• An Elementary Counterexample to the Finiteness Conjecture
• Stability of Linear Problems: Joint Spectral Radius of Sets of Matrices
• Mather sets for sequences of matrices and applications to the study of joint spectral radii
• Complex Polytope Extremality Results for Families of Matrices
• Spectral Properties of Matrices which have Invariant Cones
• Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms

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