Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms

DOI10.1016/j.laa.2010.05.007zbMath1202.15028arXiv0909.2800OpenAlexW2963060516MaRDI QIDQ5962282

Ian D. Morris

Publication date: 21 September 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.2800

zbMATH Keywords

stabilityjoint spectral radiusBarabanov normextremal normfinite irreducible set of matricesfiniteness property

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items

On the Joint Spectral Radius ⋮ Ergodic properties of matrix equilibrium states ⋮ Lyapunov-maximizing measures for pairs of weighted shift operators ⋮ The Barabanov Norm is Generically Unique, Simple, and Easily Computed ⋮ Rank-one characterization of joint spectral radius of finite matrix family ⋮ Explicit construction of a Barabanov norm for a class of positive planar discrete-time linear switched systems ⋮ The finite-step realizability of the joint spectral radius of a pair of \(d \times d\) matrices one of which being rank-one ⋮ Extremal norms for positive linear inclusions ⋮ Geometric and asymptotic properties associated with linear switched systems ⋮ Ergodic optimization in dynamical systems ⋮ Canonical Construction of Polytope Barabanov Norms and Antinorms for Sets of Matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Mañé-Conze-Guivarc'h lemma for amphidynamical systems
• Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets
• Lyapunov indicator of discrete inclusions. I
• Algebraic unsolvability of problem of absolute stability of desynchronized systems
• Bounded semigroups of matrices
• The finiteness conjecture for the generalized spectral radius of a set of matrices
• The generalized spectral radius and extremal norms
• The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate
• The fish has no bones
• The generalized spectral radius is strictly increasing
• Stability of discrete linear inclusion
• Computing the joint spectral radius
• An efficient lower bound for the generalized spectral radius of a set of matrices
• Ergodic transport theory and piecewise analytic subactions for analytic dynamics
• On the finiteness property for rational matrices
• Lyapunov minimizing measures for expanding maps of the circle
• Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
• Perturbation Bounds for Matrix Eigenvalues
• Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
• An Elementary Counterexample to the Finiteness Conjecture
• On codes that avoid specified differences
• Computationally Efficient Approximations of the Joint Spectral Radius
• Complex Polytope Extremality Results for Families of Matrices
• On the zero-stability of variable stepsize multistep methods: The spectral radius approach