Solution of parameter-varying linear matrix inequalities in Toeplitz form

Mertzios, G.B.

Solution of parameter-varying linear matrix inequalities in Toeplitz form

Mertzios, G.B.

Authors

Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor

Abstract

In this paper the necessary and suﬃcient conditions are given for the solution of a system of parameter varying linear inequalities of the form A (t) x ≥ b (t) for all t ∈ T ,where T is an arbitrary set, x is the unknown vector, A (t) is a known triangular Toeplitz matrix and b (t) is a known vector. For every t ∈ T the corresponding inequality deﬁnes a polyhedron, in which the solution should exist. The solution of the linear system is the intersection of the corresponding polyhedrons for every t ∈ T . A general modular decomposition method has been developed, which is based on the successive reduction of the initial system of inequalities by reducing iteratively the number of variables and by considering an equivalent system of inequalities

Citation

Mertzios, G. (2006). Solution of parameter-varying linear matrix inequalities in Toeplitz form. Journal of applied functional analysis, 1(2), 131-152

Journal Article Type	Article
Publication Date	Jan 1, 2006
Deposit Date	Dec 8, 2011
Publicly Available Date	Jan 4, 2012
Journal	Journal of applied functional analysis
Print ISSN	1559-1948
Electronic ISSN	1559-1956
Publisher	Eudoxus Press
Peer Reviewed	Peer Reviewed
Volume	1
Issue	2
Pages	131-152
Keywords	Linear matrix inequalities, Parameter varying systems, Constrained optimization, Polyhedron, Robust control theory, Toeplitz matrices.
Publisher URL	http://www.eudoxuspress.com