Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces

DOI10.1137/S0895479800377228zbMath1029.65044MaRDI QIDQ2784397

Volker Mehrmann, Gerhard Freiling, Hong-guo Xu

Publication date: 23 April 2002

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

zbMATH Keywords

algebraic Riccati equationeigenvalue problemHamiltonian matrixHermitian solutionssymplectic matrixLagrangian invariant subspace

Mathematics Subject Classification ID

Related Items (25)

On discrete algebraic Riccati equations: a rank characterization of solutions ⋮ Structure-preserving diagonalization of matrices in indefinite inner product spaces ⋮ Transformations between discrete-time and continuous-time algebraic Riccati equations ⋮ Characterization of solutions of non-symmetric algebraic Riccati equations ⋮ A numerical method for computing the Hamiltonian Schur form ⋮ Necessary and sufficient conditions for solvability of the Riccati inequalities in the general case ⋮ The asymptotic analysis of the structure-preserving doubling algorithms ⋮ Kalman-Popov-Yakubovich Lemma and the \(S\)-procedure: a historical essay ⋮ Imaginary axis eigenvalues of Hamiltonian matrix: controllability, defectiveness and the ϵ-characteristic ⋮ Second-order Accurate Ensemble Transform Particle Filters ⋮ ON THE PROPERTIES OF A KIND OF RANDOM MATRICES ⋮ Eigenvalue characterization of some structured matrix pencils under linear perturbation ⋮ Robust formulas for \(H_{\infty }\) optimal controllers ⋮ Unit Triangular Factorization of the Matrix Symplectic Group ⋮ A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems ⋮ Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis ⋮ A structure-preserving method for positive realness problem in control ⋮ Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods ⋮ Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations ⋮ A robust numerical method for the \(\gamma\)-iteration in \(H_{\infty}\) control ⋮ ON A PERTURBATION THEORY OF HAMILTONIAN SYSTEMS WITH PERIODIC COEFFICIENTS ⋮ Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices ⋮ Optimal Robustness of Port-Hamiltonian Systems ⋮ Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control ⋮ A new block method for computing the Hamiltonian Schur form

This page was built for publication: Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces