Premium
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.