Robust stability and a criss-cross algorithm for pseudospectra

J. V. Burke, A. S. Lewis, M. L. Overton

Research output: Contribution to journalArticle

Abstract

A dynamical system ẋ = 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 Hamiltonian matrices.

Original languageEnglish (US)
Pages (from-to)359-375
Number of pages17
JournalIMA Journal of Numerical Analysis
Volume23
Issue number3
DOIs
StatePublished - Jul 2003

Fingerprint

Pseudospectra
Robust Stability
Abscissa
Eigenvalue
Local Quadratic Convergence
Hamiltonian Matrix
Hamiltonians
Computing
Square matrix
Half-plane
Dynamical systems
Dynamical system
Norm
Robust stability

Keywords

  • Eigenvalue optimization
  • H norm
  • Hamiltonian matrix
  • Pseudospectrum
  • Robust control
  • Robust optimization
  • Spectral abscissa
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Robust stability and a criss-cross algorithm for pseudospectra. / Burke, J. V.; Lewis, A. S.; Overton, M. L.

In: IMA Journal of Numerical Analysis, Vol. 23, No. 3, 07.2003, p. 359-375.

Research output: Contribution to journalArticle

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