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A fast algorithm to compute the \(H_{\infty}\)-norm of a transfer function matrix. (English) Zbl 0699.93021
Summary: A fast algorithm is presented to compute the \(H_{\infty}\)-norm of a transfer function matrix, based on the relation between the singular values of the transfer function matrix and the eigenvalues of a related Hamiltonian matrix. The norm is computed with guaranteed accuracy. A very simple method to compute a rather close lower bound on the \(H_{\infty}\)-norm is given.

MSC:
93B40 Computational methods in systems theory (MSC2010)
93B50 Synthesis problems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
93B35 Sensitivity (robustness)
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