Bounding the Solution Set of Uncertain Linear Equations: a Convex Relaxation Approach

In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations (ULE). The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. The resulting bounding condition is expressed as a Linear Matrix Inequality (LMI) constraint on the ellipsoid parameters and the additional scaling variables. This formulation leads to a convex optimization problem that can be efficiently solved by means of interior point barrier methods.