Fast methods for estimating the distance to uncontrollability

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

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - 2006


  • 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

  • Analysis


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