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A singular values-based approach to specify the robustness of a multivariable linear feedback system in state-space representation is investigated. The robustness measure which is considered is the largest spectral norm of an additive uncertainty in the closed-loop system matrix, for which stability is guaranteed. It is shown that under the constraint of prescribed pole placement, a lower bound for the robustness measure is maximized, when the Frobenius norm of the closed-loop system matrix is minimized.
Date of Publication: May 1987