LMI approximations for the radius of the intersection of ellipsoids

Author

Henrion, Didierh ; Tarbouriech, S. ; Rzelier, Isa

Author_Institution

Lab. d´´Autom. et d´´Anal. des Syst., CNRS, Toulouse, France

Volume

2

fYear

1998

fDate

16-18 Dec 1998

Firstpage

1759

Abstract

This paper addresses the problem of evaluating the maximum norm vector within the intersection of several ellipsoids. This difficult nonconvex optimization problem frequently arises in robust control synthesis. Linear matrix inequality relaxations of the problem are enumerated. A randomized algorithm and several ellipsoidal approximations are proposed. Guaranteed approximation bounds are derived in order to evaluate the quality of these relaxations

Keywords

control system synthesis; matrix algebra; optimisation; randomised algorithms; relaxation theory; robust control; LMI approximations; ellipsoid intersection radius; ellipsoidal approximations; linear matrix inequality relaxations; maximum norm vector evaluation; nonconvex optimization; randomized algorithm; robust control synthesis; Constraint optimization; Control theory; Ellipsoids; Linear matrix inequalities; Linear programming; Quadratic programming; Robust control; Robustness; Symmetric matrices; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1998. Proceedings of the 37th IEEE Conference on

Conference_Location

Tampa, FL

ISSN

0191-2216

Print_ISBN

0-7803-4394-8

Type

conf

DOI

10.1109/CDC.1998.758550

Filename

758550