
doi: 10.1109/9.478340
Remind that the Frobenius norm of the matrix \(A\) with the items \(A_{\mu\nu}\) is \((\sum_\mu \sum_nu|A_{\mu\nu}|^2)^{1/2}\). From the authors' abstract: ``using the notion of dual norms we show that, up to a scalar multiple, the maximum singular value is the only unitarily invariant induced norm. As a special case of this result, it follows that the Frobenius matrix norm is not induced.'' The contribution is motivated by the performance analysis of a control for its ability to reject disturbances.
performance analysis of a control, matrix norms, disturbance rejection, unitarily invariant induced norm, Operator-theoretic methods, \(H^\infty\)-control, Frobenius norm, maximum singular value, Applications of operator theory in systems, signals, circuits, and control theory, dual norms
performance analysis of a control, matrix norms, disturbance rejection, unitarily invariant induced norm, Operator-theoretic methods, \(H^\infty\)-control, Frobenius norm, maximum singular value, Applications of operator theory in systems, signals, circuits, and control theory, dual norms
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