On  G eneralised  S tein's  I nequalites and the Inertias of Their Solutions: Application to Pencil Finite Root‐Clustering | Zendy

Sari B. | Zendy; Bachelier O. | Zendy; Mehdi D. | Zendy

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On G eneralised S tein's I nequalites and the Inertias of Their Solutions: Application to Pencil Finite Root‐Clustering

Author(s) -

Sari B.,

Bachelier O.,

Mehdi D.

Publication year - 2013

Publication title -

asian journal of control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.769

H-Index - 53

eISSN - 1934-6093

pISSN - 1561-8625

DOI - 10.1002/asjc.539

Subject(s) - pencil (optics) , inertia , cluster analysis , matrix pencil , mathematics , root (linguistics) , pure mathematics , physics , statistics , classical mechanics , eigenvalues and eigenvectors , linguistics , philosophy , quantum mechanics

This note deals with the inertia of the solutions to G eneralised S tein's I nequalities ( GSI ) i.e. S tein's inequalities related to discrete descriptor models described through linear matrix pencils. Only strict inequalities are considered. It is shown that, under some very slight assumptions, there always exists a solution to the GSI and some properties on the inertia of this solution can be derived very easily. As an application, the finite root‐clustering of the pencil associated with a descriptor system in a union of separate discs is considered.

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