\(h_{2}\)-norm optimal model reduction for large scale discrete dynamical MIMO systems

DOI10.1016/j.cam.2008.12.029zbMath1178.93032OpenAlexW2064610948MaRDI QIDQ1044849

J. Blot

Publication date: 15 December 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.12.029

zbMATH Keywords

rational interpolationmodel reductiontangential interpolationdiscrete-time LTI systems\(h_{2}\)-approximation

Mathematics Subject Classification ID

Factorization of matrices (15A23) Discrete-time control/observation systems (93C55) System structure simplification (93B11)

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Cites Work

• Unnamed Item
• Unnamed Item
• Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic
• Model order reduction: Theory, research aspects and applications. Selected papers based on the presentations at the workshop `Model order reduction, coupled problems and optimization', Leiden, The Netherlands, September 19--23, 2005.
• \(h_{2}\)-norm optimal model reduction for large scale discrete dynamical MIMO systems
• Linear system approximation via covariance equivalent realizations
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Synthesis of minimum roundoff noise fixed point digital filters
• Model Reduction of MIMO Systems via Tangential Interpolation
• Model reduction for multivariable systems
• Approximate Gauss–Newton methods for optimal state estimation using reduced‐order models
• Approximation of Large-Scale Dynamical Systems