Fast methods for estimating the distance to uncontrollability

M. Gu, E. Mengi, M. L. Overton, J. Xia, J. Zhu

Research output: Contribution to journalArticle

Abstract

The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.

Original languageEnglish (US)
Pages (from-to)477-502
Number of pages26
JournalSIAM Journal on Matrix Analysis and Applications
Volume28
Issue number2
DOIs
StatePublished - 2006

Fingerprint

Linear control systems
Experiments
Linear Control Systems
Numerical Experiment
Norm
Estimate

Keywords

  • Complex controllability radius
  • Distance to uncontrollability
  • Kronecker product
  • Real eigen-value extraction
  • Shift-and-invert Arnoldi
  • Shifted inverse iteration
  • Sylvester equation
  • Trisection

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis

Cite this

Fast methods for estimating the distance to uncontrollability. / Gu, M.; Mengi, E.; Overton, M. L.; Xia, J.; Zhu, J.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 28, No. 2, 2006, p. 477-502.

Research output: Contribution to journalArticle

Gu, M. ; Mengi, E. ; Overton, M. L. ; Xia, J. ; Zhu, J. / Fast methods for estimating the distance to uncontrollability. In: SIAM Journal on Matrix Analysis and Applications. 2006 ; Vol. 28, No. 2. pp. 477-502.
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