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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.

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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[1] Boyd, S.; Balakrishnan, V.; Kabamba, P., On computing the \(H∞- norm\) of a transfer function matrix, (), 396-397
[2] Boyd, S.; Balakrishnan, V.; Kabamba, P., A bisection method for computing the \(H∞- norm\) of a transfer function matrix, (), 207-219 · Zbl 0674.93020
[3] S. Boyd and V. Balakrishnan, A regularity result for the singular values of a transfer function matrix and a quadratically convergent algorithm for computing its \(L∞- norm\), Systems Control Lett. (to appear). · Zbl 0704.93014
[4] Chen, Chi-Tsong, Linear system theory and design, (1984), Holt-Saunders Japan
[5] Doyle, J.; Glover, K.; Khargonekar, P.; Francis, B., State-space solutions to standard \(H2 and H∞\) control problems, IEEE trans. automat. control, 34, 831-847, (1989) · Zbl 0698.93031
[6] Enns, D.F., Model reduction with balanced realizations: an error bound and a frequency weighted generalization, (), 127-132
[7] Francis, B.A., A course in H_{∞} control theory, (1987), Springer-Verlag Berlin-New York
[8] Glover, K., All optimal Hankel-norm approximations of linear multivariable systems and their \(L∞- error\) bounds, Internat. J. control, 39, 1115-1193, (1984) · Zbl 0543.93036
[9] Postlethwaite, I., A generalized inverse Nyquist stability criterion, Internat. J. control, 26, 325-340, (1977) · Zbl 0366.93024
[10] Robel, G., On computing the infinity norm, IEEE trans. automat. control, 34, 882-884, (1989) · Zbl 0698.93022
[11] Scherer, C., \(H∞- control\) by state feedback: an iterative algorithm and characterization of high-gain occurrence,, Systems control lett., 12, 383-391, (1989) · Zbl 0684.93032
[12] Steinbuch, M., Dynamic modelling and robust control of a wind energy conversion system, ()
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