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We propose a generalization of the Butkovskiy's method of control with compact support  allowing to derive exact controllability conditions and construct explicit solutions in control problems for systems with distributed parameters. The idea is the introduction of a new state function which is supported in considered bounded time interval and coincides with the original one therein. By means of techniques of the distributions theory the problem is reduced to an interpolation problem fordoi:10.1515/acsc-2015-0001 fatcat:2eixi6g3tzhz7kakj5g5ca7eky