On the root invariant regions structure for linear systems

E. N. Gryazina, B. T. Polyak

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Citations (Scopus)


D-decomposition technique is targeted to describe the stability domain in parameter space for linear systems, depending on parameters. The technique is very simple and effective for the case of one or two parameters. However the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail; it is the purpose of the present paper.We prove that the number of stability intervals for one real parameter is no more than n/2 (n being the degree of the characteristic polynomial) and provide an example, where this number is achieved. For one complex or two real parameters we estimate the number of root invariant regions (equal n 2-2n+3 for complex and 2n2-2n+3 for real case) and demonstrate that this upper bound is tight. The example with n-1 simply connected stability regions in 2D parameter plane is analyzed.

Original languageEnglish
Title of host publicationProceedings of the 16th IFAC World Congress, IFAC 2005
PublisherIFAC Secretariat
Number of pages6
ISBN (Print)008045108X, 9780080451084
Publication statusPublished - 2005
Externally publishedYes

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


  • Characteristic polynomials
  • Linear systems
  • Nyquist diagrams
  • Stability analysis
  • Stability domain


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