PERTURBATION THEORY FOR HAMILTONIAN MATRICES AND THE DISTANCE TO BOUNDED-REALNESS

Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2011-04, Vol.32 (2), p.484-514
Main Authors: ALAM, R, BORA, S, KAROW, M, MEHRMANN, V, MORO, J
Format: Article
Language:English
Subjects:
Algebra
Approximation
Eigenvalues
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in probability and statistics
Optimization techniques
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/10079464X