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IMA Journal of Mathematical Control and Information 2005 22(3):227-239; doi:10.1093/imamci/dni007
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© The Author 2005. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved.

An approach for robust matrix root-clustering analysis in a union of regions

Jérôme Bosche *, Olivier Bachelier § and Driss Mehdi ¶

LAII-ESIP, Bâtiment de Mécanique, 40, Avenue du Recteur Pineau, 86022 Poitiers Cedex, France

This paper addresses the problem of robust matrix root-clustering analysis in a union of regions. The considered matrices are complex and subject to both polytopic and parameter-dependent norm-bounded uncertainties. The clustering regions are unions of convex and possibly disjoint and non-symmetric subregions of the complex plane. The proposed clustering conditions are formulated in terms of linear matrix inequalities, which enables an easy computation of Lyapunov matrices (possibly parameterdependent) that ensure the clustering property. The results are an improvement of a previous result from the two last authors. Some connections to classical results of the literature are also provided.

Keywords: matrix root-clustering; union of regions; DR-stability; DU-stability; LMI; parameter-dependent Lyapunov matrix.

* Email: Jerome.Bosche{at}univ-poitiers.fr

§ Email: Olivier.Bachelier{at}univ-poitiers.fr

Email: Driss.Mehdi{at}univ-poitiers.fr

Received on 30 September 2003.


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