Robust D-stability analysis of uncertain polynomial matrices via polynomial-type multipliers

Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)


This paper addresses robust D-stability analysis problems of uncertain polynomial matrices. The underlying idea we follow is that a given polynomial matrix is D-stable if and only if there exist polynomial-type multipliers that render the resulting polynomial matrices to be strictly positive over a specific region on the complex plane. By applying the generalized S-procedure technique, we show that those positivity analysis problems can be reduced into feasibility tests of linear matrix inequalities (LMIs). Thus we can obtain varieties of LMI conditions for (robust) D-stability analysis of polynomial matrices according to the degree/structure of the multipliers to be employed. in particular, we show that existing LMI conditions for robust D-stability analysis can be viewed as particular cases of the proposed conditions, where the degree of the multipliers chosen to be the same as those of the polynomial matrices to be examined. It turns out that, by increasing the degree of the multipliers, we can readily obtain less conservative LMI conditions than the one found in the literature.

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

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


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