Generalized matrix diagonal stability and linear dynamical systems

DOI10.1016/j.laa.2006.04.021zbMath1125.93058OpenAlexW2081519448MaRDI QIDQ865394

Mihail Voicu, Octavian Pastravanu

Publication date: 14 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.04.021

zbMATH Keywords

invariant setslinear dynamical systems(diagonally invariant) exponential stabilityGershgorin's disksStein/Lyapunov matrix inequality(essentially) nonnegative matricesmatrix diagonal stability

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Symmetries, invariants of ordinary differential equations (34C14) Asymptotic stability in control theory (93D20) Stability of solutions to ordinary differential equations (34D20) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Linear ordinary differential equations and systems (34A30)

Related Items (15)

On the existence of a common Lyapunov function for a family of nonlinear positive systems ⋮ Computation of the monodromy matrix in floating point arithmetic with the Wilkinson model ⋮ The Yakubovich S-Lemma Revisited: Stability and Contractivity in Non-Euclidean Norms ⋮ Sensitivity of Schur stability of monodromy matrix ⋮ Diagonally invariant exponential stability and stabilizability of switching linear systems ⋮ Unnamed Item ⋮ Further results on diagonally invariant exponential stability of switching linear systems ⋮ Linear time-variant systems: Lyapunov functions and invariant sets defined by Hölder norms ⋮ Novel estimations for the eigenvalue bounds of complex interval matrices ⋮ Sufficient conditions for Schur and Hurwitz diagonal stability of complex interval matrices ⋮ Invariance properties of interval dynamical systems ⋮ Stability of matrix polytopes with a dominant vertex and implications for system dynamics ⋮ Diagonal stability of interval matrices and applications ⋮ \((M, \beta)\)-stability of positive linear systems ⋮ Sensitivity of Hurwitz stability of linear differential equation systems with constant coefficients

Cites Work

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• Componentwise stability of 1D and 2D linear discrete-time systems
• Transformations by diagonal matrices in a normed space
• Componentwise asymptotic stability of linear constant dynamical systems
• Matrix Analysis
• Vector norms as Lyapunov functions for linear systems
• On the componentwise stability of linear systems

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