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Some problems in optimal control, for a class of linear distributed parameter systems, are posed. By using a theorem of approximation theory, a maximum principle, which is applicable to these optimal control problems, is given. It is shown, that for the problems posed in this paper, this maximum principle is an extension of Butkovskii's maximum principle and of Demyanov and Rubinov's theorem. In addition, two optimal control problems, in linear lumped parameter systems are posed. For thesedoi:10.1016/s0022-0000(69)80005-x fatcat:uejranp5gjf5teys74dgvl5kpq