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A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its \(L_{\infty}\)-norm. (English) Zbl 0704.93014
Summary: The i-th singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singular value has a Lipschitz second derivative, but need not have a third derivative. Using this regularity result, we give a quadratically convergent algorithm for computing the \(L_{\infty}\)-norm of a transfer matrix.

MSC:
93B36 \(H^\infty\)-control
93B40 Computational methods in systems theory (MSC2010)
15A18 Eigenvalues, singular values, and eigenvectors
93C35 Multivariable systems, multidimensional control systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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