Title :
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
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;
Conference_Titel :
Decision and Control, 1998. Proceedings of the 37th IEEE Conference on
Conference_Location :
Tampa, FL
Print_ISBN :
0-7803-4394-8
DOI :
10.1109/CDC.1998.758550
