A formula for computation of the real stability radius

DOI10.1016/0005-1098(95)00024-QzbMath0839.93039OpenAlexW2050649877MaRDI QIDQ1898494

John C. Doyle, Li Qiu, Edward Joseph Davison, Anders Rantzer, Bo Bernhardsson, Peter M. Young

Publication date: 23 June 1996

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0005-1098(95)00024-q

zbMATH Keywords

sensitivityrobustnessperturbation matrixreal stability radiusrobust pole placement

Mathematics Subject Classification ID

Sensitivity (robustness) (93B35) Perturbations in control/observation systems (93C73) Eigenvalue problems (93B60) Pole and zero placement problems (93B55) Eigenvalues, singular values, and eigenvectors (15A18)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability radius for structured perturbations and the algebraic Riccati equation
• A simple procedure for the exact stability robustness computation of polynomials with affine coefficient perturbations
• The stability robustness determination of state space models with real unstructured perturbations
• Analytic perturbation theory for matrices and operators. Licensed ed
• Stability radii of linear systems
• Matrix Analysis
• State-space measures for stability robustness
• A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices
• Multivariable feedback design: Concepts for a classical/modern synthesis
• Necessary and sufficient condition for robust stability of linear distributed feedback systems†
• When are the complex and the real stability radii equal?

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