Invariance of characteristic values and \(L_\infty\) norm under lossless positive real transformations

DOI10.1016/J.JFRANKLIN.2016.03.019zbMath1347.93140OpenAlexW2319763330MaRDI QIDQ328027

Mattia Frasca, Arturo Buscarino, Maria G. Xibilia, Luigi Fortuna

Publication date: 20 October 2016

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2016.03.019

zbMATH Keywords

linear time-invariant (LTI) systems\(L_\infty\) normalgebraic Riccati equations (AREs)

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Transformations (93B17)

Related Items (6)

Continuous time LTI systems under lossless positive real transformations: open-loop balanced representation and truncated reduced-order models ⋮ Positive-real systems under lossless transformations: invariants and reduced order models ⋮ The structure of characteristic values for classes of linear time-invariant systems ⋮ Necessary and sufficient conditions for lossless negative imaginary systems ⋮ Nyquist plots under frequency transformations ⋮ New sufficient condition for the positive definiteness of fourth order tensors

Cites Work

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• Invariance of second-order modes under frequency transformation in 2-D separable denominator digital filters
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• A direct method for computing the \(L^{\infty}\) norm of a transfer matrix
• A new set of invariants for linear systems--Application to reduced order compensator design
• On Deriving the Inverse of a Sum of Matrices
• LQG balancing and reduced LQG compensation of symmetric passive systems†

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