Using permuted graph bases in \(\mathcal{H}_\infty\) control

DOI10.1016/j.automatica.2013.02.039zbMath1360.93224OpenAlexW2061729649MaRDI QIDQ522828

Federico Poloni, Volker Mehrmann

Publication date: 19 April 2017

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2013.02.039

zbMATH Keywords

robust controlalgebraic Riccati equationsnumerical algorithmsinverse-free algorithmsmatrix sign iteration

Mathematics Subject Classification ID

Applications of graph theory (05C90) Sensitivity (robustness) (93B35) (H^infty)-control (93B36)

Related Items (2)

An inverse‐free ADI algorithm for computing Lagrangian invariant subspaces ⋮ Duality of matrix pencils, Wong chains and linearizations

Uses Software

• SLICOT
• Robust Control Toolbox
• PGDoubling
• mftoolbox

Cites Work

• Lur'e equations and even matrix pencils
• Robust formulas for \(H_{\infty }\) optimal controllers
• A structured staircase algorithm for skew-symmetric/symmetric pencils
• A robust numerical method for the \(\gamma\)-iteration in \(H_{\infty}\) control
• An improved algorithm for the computation of Kronecker's canonical form of a singular pencil
• The autonomous linear quadratic control problem. Theory and numerical solution
• Parallel algorithm for solving some spectral problems of linear algebra
• An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems
• Well-conditioned computations for \(H^ \infty\) controller near the optimum
• A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations
• An arithmetic for matrix pencils: theory and new algorithms
• Necessary and sufficient conditions for optimality for singular control problems: A transformation approach
• Structured Condition Numbers for Invariant Subspaces
• Simplifying theH∞ theory via loop-shifting, matrix-pencil and descriptor concepts
• Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
• Nonlinear multigrid for the solution of large‐scale Riccati equations in low‐rank and ℋ︁‐matrix format
• The Modified Optimal $\mathcal{H}_\infty$ Control Problem for Descriptor Systems
• On the Game Riccati Equations Arising in $H_\infty $ Control Problems
• Numerically Reliable Computation of Optimal Performance in Singular $H_{\inf}$ Control
• Doubling Algorithms with Permuted Lagrangian Graph Bases
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Functions of Matrices
• Control theory for linear systems
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