Result: Robust stability and a criss-cross algorithm for pseudospectra
Title:
Robust stability and a criss-cross algorithm for pseudospectra
Authors:
Source:
IMA journal of numerical analysis. 23(3):359-375
Publisher Information:
Oxford: Oxford University Press, 2003.
Publication Year:
2003
Physical Description:
print, 19 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Programmation mathématique, Mathematical programming, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Automatique théorique. Systèmes, Control theory. Systems, Analyse des systèmes de commande, Control system analysis, Calcul matriciel, Matrix calculus, Cálculo de matrices, Commande robuste, Robust control, Control robusta, Convergence numérique, Numerical convergence, Convergencia numérica, Coupe transversale, Cross section, Corte transverso, Matrice carrée, Square matrix, Matriz cuadrada, Matrice hamiltonienne, Hamiltonian matrix, Matriz hamiltoniana, Optimisation, Optimization, Optimización, Programmation mathématique, Mathematical programming, Programación matemática, Simulation numérique, Numerical simulation, Simulación numérica, Système dynamique, Dynamical system, Sistema dinámico, Abscisse spectrale, Spectral abscissa, Norme H infinie, H infinite norm, Optimisation valeur propre, Eigenvalue optimization, Pseudospectre, Pseudospectrum
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, University of Washington, Seattle, WA 98195, United States
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States
ISSN:
0272-4979
Rights:
Copyright 2003 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Operational research. Management
Mathematics
Operational research. Management
Accession Number:
edscal.14923286
Database:
PASCAL Archive
Further Information
A dynamical system x = Ax is robustly stable when all eigenvalues of complex matrices within a given distance of the square matrix A lie in the left half-plane. The 'pseudospectral abscissa', which is the largest real part of such an eigenvalue, measures the robust stability of A. We present an algorithm for computing the pseudospectral abscissa, prove global and local quadratic convergence, and discuss numerical implementation. As with analogous methods for calculating H∞norms, our algorithm depends on computing the eigenvalues of associated Flamiltonian matrices.