A robust numerical method for the \(\gamma\)-iteration in \(H_{\infty}\) control

DOI10.1016/j.laa.2007.03.026zbMath1124.93022OpenAlexW2093125373MaRDI QIDQ998193

Volker Mehrmann, Ralph Byers, Peter Benner, Hong-guo Xu

Publication date: 27 August 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.2007.03.026

zbMATH Keywords

algebraic Riccati equation\(H_{\infty}\) controlLagrangian subspaceseven matrix pencilCS decomposition

Mathematics Subject Classification ID

Related Items (17)

Finite-Dimensional Indefinite Inner Product Spaces and Applications in Numerical Analysis ⋮ On the sign characteristics of Hermitian matrix polynomials ⋮ Low-rank updates and divide-and-conquer methods for quadratic matrix equations ⋮ An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems ⋮ Eigenvalue characterization of some structured matrix pencils under linear perturbation ⋮ Ralph Byers 1955--2007 ⋮ Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithm ⋮ Robust formulas for \(H_{\infty }\) optimal controllers ⋮ A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems ⋮ Some numerical considerations in \(\mathcal{H}_\infty\) control ⋮ Using permuted graph bases in \(\mathcal{H}_\infty\) control ⋮ Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations ⋮ An inverse‐free ADI algorithm for computing Lagrangian invariant subspaces ⋮ A structure-preserving method for positive realness problem in control ⋮ Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations ⋮ Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control ⋮ A new block method for computing the Hamiltonian Schur form

Uses Software

• Matlab
• SLICOT
• Control System Toolbox
• Robust Control Toolbox

Cites Work

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