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The plant-parameter variation problem in multivariable linear systems described by state-vector equations is formulated using a new sensitivity measure. This formulation involves a direct comparison of open-loop and state-feedback performance in the presence of parameter variations and provides a basis for guaranteeing the superiority of the feedback design. Results are obtained for both continuous and discrete multi-input, multi-output systems. Furthermore, it is shown for single-input, multi-output plants that a low-sensitivity design is also an optimal feedback-control design with respect to a quadratic performance index. This provides a new interpretation of a similar result previously obtained by Kalman.
Perkins et al. (Mon,) studied this question.