Recent stability issues for linear dynamical systems

• Verfasst von: Gillis, Nicolas [VerfasserIn]
• Verfasst von: Guglielmi, Nicola [VerfasserIn] [HerausgeberIn]
• Verfasst von: Lubich, Christian [VerfasserIn] [HerausgeberIn]
• Verfasst von: Mehrmann, Volker [VerfasserIn]
• Verfasst von: Sharma, Punit [VerfasserIn]
• Verfasst von: Vandereycken, Bart [VerfasserIn]
• Titel: Recent stability issues for linear dynamical systems
• Titelzusatz: Cetraro, Italy 2021
• Körperschaft: CIME Summer School on Applied Mathematics "Recent stability issues for linear dynamical systems. Matrix nearness problems and eigenvalue optimization" <2021, Cetraro> [VerfasserIn]
• Institutionen: Springer Nature Switzerland AG [Verlag]
• Verf.angabe: Nicolas Gillis, Nicola Guglielmi, Christian Lubich, Volker Mehrmann, Punit Sharma, Bart Vandereycken ; Nicola Guglielmi, Christian Lubich, editors
• Verlagsort: Cham
• Verlag: Springer
• E-Jahr: 2024
• Jahr: [2024]
• Umfang: xi, 174 Seiten
• Illustrationen: Illustrationen, Diagramme
• Gesamttitel/Reihe: Lecture notes in mathematics ; volume 2357 : CIME Foundation subseries
• Fussnoten: "This volume is the outgrowth of lectures presented during the CIME Summer School on Applied Mathematics, "Recent stability issues for linear dynamical systems. Matrix nearness problems and eigenvalue optimization", held in Cetraro (Italy) in September 2021 ..." ; Includes bibliographical references
• ISBN: 978-3-031-71325-5
• ISBN: 978-3-031-71327-9
• Dokumenttyp: Konferenzschrift
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Online-Ausgabe: Gillis, Nicolas: Recent Stability Issues for Linear Dynamical Systems. - 1st ed. 2024.. - Cham : Springer Nature Switzerland, 2024. - 1 Online-Ressource(XI, 176 p. 18 illus., 15 illus. in color.)
• K10plus-PPN: 1914892380

Abstract

This book concerns matrix nearness problems in the framework of spectral optimization. It addresses some current research directions in spectral-based stability studies for differential equations, with material on ordinary differential equations (ODEs), differential algebraic equations and dynamical systems. Here, ‘stability’ is interpreted in a broad sense which covers the need to develop stable and reliable algorithms preserving some qualitative properties of the computed solutions, methodologies which are helpful to assess the onset of potential instabilities or loss of robustness, and tools to determine the asymptotic properties of the solution or its discretization. The topics considered include the computation of robustness measures for linear problems, the use of low-rank ODEs to approximate such measures via gradient systems, the regularity, stability, passivity and controllability analysis of structured linear descriptor systems, and the use of acceleration techniques to deal with some of the presented computational problems. Although the emphasis is on the numerical study of differential equations and dynamical systems, the book will also be of interest to researchers in matrix theory, spectral optimization and spectral graph theory, as well as in dynamical systems and systems theory.