Degree Bounds for Polynomial Verification of the Matrix Cube Problem

In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semi-algebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz refutations. When the semi-algebraic set is a hypercube, we gi...

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Bibliographic Details
Published inProceedings of the 45th IEEE Conference on Decision and Control pp. 4405 - 4410
Main Authors Been-Der Chen, Lall, S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2006
Subjects
Hypercubes
Linear matrix inequalities
Matrix converters
Polynomials
Robust control
Stability
Sufficient conditions
Symmetric matrices
Testing
Uncertainty
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Summary:In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semi-algebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz refutations. When the semi-algebraic set is a hypercube, we give bounds on the degree of the required certificate polynomials
ISBN:9781424401710
1424401712
ISSN:0191-2216
DOI:10.1109/CDC.2006.376783