Pseudospectral components and the distance to uncontrollability

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

Research output: Contribution to journalArticlepeer-review


We show that 2-norm pseudospectra of m-by-n matrices have no more than 2m(4m-1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu's recent algorithm, and we show how these may be used to locally maximize the distance to uncontrollability for a parameterized system.

Original languageEnglish (US)
Pages (from-to)350-361
Number of pages12
JournalSIAM Journal on Matrix Analysis and Applications
Issue number2
StatePublished - 2005


  • Connected components
  • Distance to uncontrollability
  • Pseudospectrum
  • Robust control
  • Trisection

ASJC Scopus subject areas

  • Analysis


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