Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices

DOI10.1080/03081080701452508zbMath1163.15030OpenAlexW2030038021MaRDI QIDQ3615519

Volker Mehrmann, Christian Mehl, André C. M. Ran, Leiba Rodman

Publication date: 20 March 2009

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

Full work available at URL: https://doi.org/10.1080/03081080701452508

zbMATH Keywords

stabilitycanonical formsconditional stabilityperturbation analysisHamiltonian matrixsymplectic matrixLagrangian invariant subspace

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Perturbations in control/observation systems (93C73) Hermitian, skew-Hermitian, and related matrices (15B57) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21)

Related Items

The Algebraic Riccati Equation and Its Role in Indefinite Inner Product Spaces, Linear constraint problem of Hermitian unitary symplectic matrices, Stability of invariant subspaces of quaternion matrices, Structure Preserving Model Reduction of Parametric Hamiltonian Systems, Lipschitz properties of structure preserving matrix perturbations, Exact low-order polynomial expressions to compute the Kolmogoroff–Nagumo mean in the affine symplectic group of optical transference matrices, Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations, ON A PERTURBATION THEORY OF HAMILTONIAN SYSTEMS WITH PERIODIC COEFFICIENTS, A class of nilpotent Lie algebras whose center acts nontrivially in cohomology

Cites Work

• Unnamed Item
• Unnamed Item
• Pencils of complex and real symmetric and skew matrices
• Stability of neutral invariant subspaces in indefinite inner products and stable symmetric factorizations
• Stability of invariant maximal semidefinite subspaces. II. Applications: Self-adjoint rational matrix functions, algebraic Riccati equations
• Spectral analysis of selfadjoint matrix polynomials
• Stable hermitian solutions of discrete algebraic Riccati equations
• Stable factorizations of monic matrix polynomials and stable invariant subspaces
• The rate of convergence of real invariant subspaces
• Canonical form of symplectic matrix pencils
• A step toward a unified treatment of continuous and discrete time control problems
• Canonical forms for Hamiltonian and symplectic matrices and pencils
• Stability of invariant maximal semidefinite subspaces. I
• Similarity vs unitary similarity and perturbation analysis of sign characteristics: complex and real indefinite inner products
• Canonical forms for complex matrix congruence and \(^{*}\)-congruence
• Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence
• Perturbation Analysis of Hamiltonian Schur and Block-Schur Forms
• Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces
• Congruences and Norms of Hermitian Matrices
• State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
• Structured Eigenvalue Condition Number and Backward Error of a Class of Polynomial Eigenvalue Problems
• On Stability of Invariant Subspaces of Matrices
• Canonical forms for symplectic and Hamiltonian matrices
• Stability index of invariant subspaced of matrices
• Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory