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It is shown that every linear system with nondynamic feedback is optimal with respect to a quadratic performance index that includes a cross-product term between the state and control. If the index is further generalized to include derivatives of the control, every (sufficiently smooth) linear finite-dimensional dynamic feedback and feedforward control system is optimal. Methods of constructing all such indices are indicated, and some practical implications are discussed.
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Kreindler et al. (1972) studied this question.
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