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This paper deals with further advances of the author's recent work on optimal design of control systems and Wiener filters. Specifically, we consider the problem of designing a system to control a plant when (1) not all state variables are measurable, (2) the measured state variables are contaminated with noise, and (3) there are random disturbances. An explicit design procedure (well adapted to digital computation) is presented. In addition, some fundamental new concepts (controllability, observability, etc.) are introduced. A general theory of control systems is outlined which answers many basic questions (what is controllable? why? how?) and gives a highly efficient method of computation. This paper is to be published in the Proceedings of the First IFAC Moscow Congress by Butterworth Scientific Publications in 1960.