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In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.doi:10.2478/amcs-2014-0053 fatcat:fod2rhvlt5ejvcfcywsdq3qzn4