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On the structured distance to uncontrollability

by M. Karow and D. Kressner

(Report number 2008-19)

Abstract
This article is concerned with the structured distance to uncontrollability of a linear time-invariant system and relates this concept to a variation of the $\mu$-value. The developed framework is applied to derive computational expressions for the class of real perturbations as well as for Hermitian, symmetric, and skew-symmetric perturbations in a relatively simple manner. Examples demonstrate that the structured distance can differ from the standard, unstructured distance to uncontrollability by an arbitrary amount. It is also shown how systems of higher order can be addressed.

Keywords:

@Techreport{KK08_383,
  author = {M. Karow and D. Kressner},
  title = {On the structured distance to uncontrollability},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-19},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-19.pdf },
  year = {2008}
}

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