Techniques for the optimum synthesis of multipole control systems with random processes as inputs

This report considers the general problem of obtaining the optimum multipole system when the inputs to the system are stationary random processes. The system under investigation is linear and time invariant. The input to each terminal shall consist of signal and noise. The synthesis procedure is carried out under the basis that a fixed plant must be compensated in order to perform certain desired tasks. The design criterion employed is the minimum mean square error between actual outputs and ideal outputs of the system. A set of integral equations shall be obtained, which can be converted into algebraic equations through transformation. By solving these equations and using the method of undetermined coefficients, the transfer functions of the compensation can be uniquely determined.