LMI approximations for the radius of the intersection of ellipsoids

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.

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