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A method is developed for the systematic synthesis of multipole control systems which is based on the application of certain system constraints. These constraints reduce the degrees of freedom of the system without, however, resulting in an undue restriction on system performance. A system transfer matrix is described which characterizes the system. Through the application of the constraints it becomes possible to solve this matrix for the controller transfer functions required to achieve specified performance. This permits the synthesis of multipole control systems in a manner similar to that presently possible for single-input single-output system.