Constructing a homogeneous LTI descriptor system with desired properties using perturbation theory

Athanasios A. Pantelous, Athanasios D. Karageorgos, Grigoris I. Kalogeropoulos

Research output: Contribution to journalArticleResearchpeer-review


In the literature regarding linear systems and mathematical control theory, several different techniques have been developed for obtaining the solution of homogeneous linear time-invariant (LTI) descriptor differential systems. In this article, applying the complex Weierstrass canonical form, we investigate the conditions under which a descriptor system with a specific structure and desired properties is being constructed using perturbation theory. Our approach is very general, and as an example, a stable homogeneous LTI descriptor system is designed. Thus, a proportional and derivative controller can be used, such as the case where a family of perturbed pencils is defined and the solutions of the initial and the relative perturbed systems are ρM(t)-close with respect to a Frobenius distance. A Step-algorithm and an illustrative example are also presented to illustrate the results of this article.

Original languageEnglish
Pages (from-to)1915-1925
Number of pages11
JournalInternational Journal of Control
Issue number11
Publication statusPublished - 1 Nov 2011
Externally publishedYes


  • linear descriptor systems
  • matrix pencil theory
  • perturbation theory

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