Recent stability issues for linear dynamical systems : Cetraro, Italy 2021 / Nicolas Gillis, Nicola Guglielmi, Christian Lubich, Volker Mehrmann, Punit Sharma, Bart Vandereycken ; Nicola Guglielmi, Christian Lubich, editors.

Format:

Book

Author/Creator:

Gillis, Nicolas, author.

Guglielmi, Nicola, author, editor.

Lubich, Christian, 1959- author, editor.

Mehrmann, V. L. (Volker Ludwig), 1955- author.

Sharma, Punit, author.

Vandereycken, Bart, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2357.

Lecture notes in mathematics (Springer-Verlag). CIME Foundation subseries 0075-8434

Lecture notes in mathematics, 0075-8434 ; volume 2357. C.I.M.E. foundation subseries, 2946-1812

Language:

English

Subjects (All):

Differential equations.

Dynamics.

Physical Description:

xi, 174 pages : illustrations (color) ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2024]

Summary:

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.

Contents:

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.

Notes:

"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."--Introduction.

Includes bibliographical references.

ISBN:

9783031713255

3031713257

OCLC:

1485323651