A rational deterministic design procedure is presented for a class of distributed parameter multivariable plants described by linear scalar differential equations. The Galerkin projection method is employed to form an approximate finite dimensional plant model. The subsequent solution of a quadratic regulator problem for the finite dimensional model results in a lumped multivariable controller which operates on the inputs and outputs of the actual plant. A deterministic observer is constructed to estimate the model state. Techniques for optimal location of the input zones and output transducers are developed. Two examples are presented.
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Orner et al. (1971) studied this question.