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All optimal Hankel-norm approximations of linear multivariable systems and their L,∞-error bounds†
Abstract
The problem of approximating a multivariable transfer function G(s) of McMillan degree n, by Ĝ(s) of McMillan degree k is considered. A complete characterization of all approximations that minimize the Hankel-norm is derived. The solution involves a characterization of all rational functions Ĝ(s) + F(s) that minimize where Ĝ(s) has McMillan degree k, and F(s) is anticavisal. The solution to the latter problem is via results on balanced realizations, all-pass functions and the inertia of matrices, all in terms of the solutions to Lyapunov equations. It is then shown that where σ k+1(G(s)) is the (k+l)st Hankel singular value of G(s) and for one class of optimal Hankel-norm approximations. The method is not computationally demanding and is applied to a 12-state model.
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Cited by
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Hara, S., Yamamoto, Y., Omata, T., & Nakano, M. (1988) · IEEE Transactions on Automatic Control · doi:10.1109/9.1274 · Cited by 1,407
Approximation of Large-Scale Dynamical Systems: An Overview
Antoulas, A. C. (2004) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)31584-7 · Cited by 377
Subspace-based signal analysis using singular value decomposition
Van Der Veen, A.-J., Deprettere, E. F., & Swindlehurst, A. L. (1993) · Proceedings of the IEEE · doi:10.1109/5.237536 · Cited by 348
Yondo, R., Andrés, E., & Valero, E. (2018) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2017.11.003 · Cited by 311
Metadata
- Authors
- GLOVER, K.
- Venue
- International Journal of Control
- Publisher
- Informa UK Limited
- Published
- 1984-06
- Volume
- 39
- Issue
- 6
- Pages
- 1115-1193
- ISSN
- 0020-7179 (ISSN-L)
- 1366-5820
- OpenAlex
- W1984714339
- Cited by
- 2,873
- References
- 0
- FWCI
- 131.94
- Type
- journal article
- Language
- en
- Open access
- closed
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- GLOVER, K. (1984). All optimal Hankel-norm approximations of linear multivariable systems and their L,∞-error bounds†. International Journal of Control. https://doi.org/10.1080/00207178408933239
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