LMI Approximations for the Radius of the Intersection of Ellipsoids: Survey

This paper surveys various linear matrix inequality relaxation techniques for evaluating the maximum norm vector within the intersection of several ellipsoids. This difficult nonconvex optimization problem arises frequently in robust control synthesis. Two randomized algorithms and several ellipsoidal approximations are described. Guaranteed approximation bounds are derived in order to evaluate the quality of these relaxations.

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