Robust formulas for \(H_{\infty }\) optimal controllers

DOI10.1016/j.automatica.2011.09.013zbMath1252.93047OpenAlexW2039485372MaRDI QIDQ665189

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

Publication date: 5 March 2012

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2011.09.013

zbMATH Keywords

controller designoptimal controllerLagrangian subspacesCS decomposition\(H_{\infty }\)-controleven pencil

Mathematics Subject Classification ID

Related Items (7)

On the sign characteristics of Hermitian matrix polynomials ⋮ Fixed-order H-infinity controller design for port-Hamiltonian systems ⋮ New approach on solving control problems with descriptor systems ⋮ Using permuted graph bases in \(\mathcal{H}_\infty\) control ⋮ An inverse‐free ADI algorithm for computing Lagrangian invariant subspaces ⋮ Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations ⋮ ${\mathscr H}_\infty$ Problem with Nonstrict Inequality and All Solutions: Interpolation Approach

Uses Software

• SLICOT
• Robust Control Toolbox

Cites Work

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• A robust numerical method for the \(\gamma\)-iteration in \(H_{\infty}\) control
• A Schur decomposition for Hamiltonian matrices
• An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems
• An arithmetic for matrix pencils: theory and new algorithms
• Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces
• The Modified Optimal $\mathcal{H}_\infty$ Control Problem for Descriptor Systems
• Numerically Reliable Computation of Optimal Performance in Singular $H_{\inf}$ Control
• Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils
• Evaluating products of matrix pencils and collapsing matrix products
• Control theory for linear systems

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