Hankel Singular Values and Vectors of a Class of Infinite-Dimensional Systems: Exact Hamiltonian Formulas for Control and Approximation Problems |
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Authors: | Yoshito Ohta |
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Affiliation: | (1) Department of Computer-Controlled Mechanical Systems, Osaka University, Suita, Osaka 565-0871, Japan. ohta@mech.eng.osaka-u.ac.jp., JP |
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Abstract: | This paper derives exact formulas for singular values and vectors of Hankel operators whose symbol is a product of a single-input
single-output inner function and a multi-input multi-output rational function. This class of Hankel operators arises from
the sensitivity minimization H
∞ control problem with a rational weight function and the approximation problem of transfer functions having rational outer
parts. It is shown that there is a Hamiltonian transcendental equation characterizing singular values which leads to a matrix
function formula for singular vectors.
Date received: May 12, 1998. Date revised: May 14, 1999. |
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Keywords: | , Hankel operator, Hankel singular value, Hankel singular vector, Model reduction, Infinite-dimensional systems,,,,,,Inner function, |
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