Computation of the singular values of Toeplitz operators and the gap metric |
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| Authors: | Kentaro Hirata Yutaka Yamamoto Allen Tannenbaum |
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| Affiliation: | a Department of Electrical and Electronic Systems, College of Engineering, Osaka Prefecture University, Osaka, 599-8531, Japan;b Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Infomatics, Kyoto University, Kyoto 606-8501, Japan;c Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455, USA |
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| Abstract: | It is widely recognized that the computation of gap metric is equivalent to a certain two-block 
problem, i.e., the gap is equal to the norm of a certain two-block operator. However, it can also be characterized as the smallest singular value of a certain Toeplitz operator. This paper derives a simple computational method for finding such singular values and the gap between two plants by using a state space approach. |
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| Keywords: | Gap metric Two-block problem Skew Toeplitz theory Toeplitz operator Hamiltonian |
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