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This paper is devoted to the controllability analysis of a class of linearcontrol systems in a Hilbert space. It is proposed to use the minimum energycontrols of a reduced lumped parameter system for solving the infinitedimensional steering problem approximately. Sufficient conditions of theapproximate controllability are formulated for a modal representation of aflexible structure with small damping.

Modal approach to the controllability problem of distributed parameter systems with damping