Recent Stability Issues for Linear Dynamical Systems

• Verfasst von: Gillis, Nicolas [VerfasserIn]
• Verfasst von: Guglielmi, Nicola [VerfasserIn]
• Verfasst von: Lubich, Christian [VerfasserIn]
• 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
• Verf.angabe: by Nicolas Gillis, Nicola Guglielmi, Christian Lubich, Volker Mehrmann, Punit Sharma, Bart Vandereycken ; edited by Nicola Guglielmi, Christian Lubich
• Ausgabe: 1st ed. 2024.
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Jahr: 2024
• Umfang: 1 Online-Ressource(XI, 176 p. 18 illus., 15 illus. in color.)
• Gesamttitel/Reihe: Lecture notes in mathematics ; 2357 : C.I.M.E. Foundation Subseries
• ISBN: 978-3-031-71326-2
• DOI: doi:10.1007/978-3-031-71326-2
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Gillis, Nicolas: Recent stability issues for linear dynamical systems. - Cham : Springer, 2024. - xi, 174 Seiten
• K10plus-PPN: 1912792745
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Introduction -- Chapter 1. Solving Matrix Nearness Problems via Hamiltonian Systems, Matrix Factorization and Optimisation -- Chapter 2. Eigenvalue Optimization and Matrix Nearness Problems via Constrained Gradient Systems -- Chapter 3. Regularity, Stability, Passivity and Controllability of Structured Linear Descriptor Systems -- Chapter 4. Algorithms for Eigenvalue Optimization Related to Stability of Dynamical Systems.

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.