On a class of generalized eigenvalue problems and equivalent eigenvalue problems that arise in systems and control theory

DOI10.1016/j.automatica.2010.10.009zbMath1219.93044OpenAlexW2053327966MaRDI QIDQ716116

Martin Corless, Robert N. Shorten

Publication date: 19 April 2011

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2010.10.009

zbMATH Keywords

passivitypositive realnessfrequency domain inequalitiesgeneralised eigenvalue problems

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Discrete-time control/observation systems (93C55) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Eigenvalue problems (93B60)

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Cites Work

• A structured staircase algorithm for skew-symmetric/symmetric pencils
• A bisection method for computing the \(H_{\infty}\) norm of a transfer matrix and related problems
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• Eigenvalue-based characterization and test for positive realness of scalar transfer functions
• Passivity Enforcement via Perturbation of Hamiltonian Matrices
• On the Characterization of Strict Positive Realness for General Matrix Transfer Functions