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The square of the
Hilbert-Schmidt norm of the Hankel operator associated with a linear system is the sum of squares of the Hankel singular values of this system. Moreover, the area enclosed by the oriented
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32:, in which high energy states are retained while low energy states are discarded. The reduced model retains the important features of the original model.
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and strictly proper linear system is equal π times the square of the
Hilbert-Schmidt norm of the Hankel operator associated with this system.
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147:"The area enclosed by the (oriented) Nyquist diagram and the Hilbert-Schmidt-Hankel norm of a linear system"
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Hankel singular values also provide the optimal range of analog filters.
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239:"Necessary and sufficient conditions for balancing unstable systems"
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Hankel singular values are calculated as the square roots, {σ
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276:Approximation of Large-Scale Dynamical Systems
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200:IEEE Transactions on Circuits and Systems
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237:Kenney, C.; Hewer, G. (Feb 1987).
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67:}, for the product of the
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30:balanced model reduction
284:10.1137/1.9780898718713
272:Antoulas, Athanasios C.
194:Groenewold, G. (1991).
69:controllability Gramian
22:Hankel singular values
80:observability Gramian
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145:Hanzon, B. (1992).
293:978-0-89871-529-3
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26:Hermann Hankel
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105:BIBO stable
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249:(2): 157.
231:References
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93:Properties
78:, and the
49:}, of the
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181:0018-9286
313:Category
278:. SIAM.
274:(2005).
115:See also
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103:of an
298:S2CID
132:Notes
288:ISBN
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16:In
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