Abstract
This paper treats balanced realization problems within the framework of canonical variate analysis. By applying the concepts of statistical studies, duality diagrams, and the RV-coefficient to deterministic systems, it is shown how both the identification (Hankel approach) and transformation (Grammian approach) based balanced realization problems lead to dual interpretations. It is further shown that both approaches lead to a minimum distance problem (equivalently maximum RV-coefficient) between certain observability and controllability properties of a linear system. The motivation for this optimization problem follows from the singular value decomposition, the orthogonal procrustes problem, and the RV-coefficient. The solution has the format of a generalized singular value decomposition.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Cailliez and J. P. Pages. “Introduction a l’analyse des données, Smash, Paris, 1976.
Y. Escoufier and P. Robert. “Choosing variables and metrics by optimizing the RV-coefficient, in: Opt. Meth. in Statistics, Academic Press, pp. 205–209, 1979.
J. A. Ramos and E. I. Verriest. “A unifying tool for comparing stochastic realization algorithms and model reduction techniques, Proc. 1984 ACC.
J. A. Ramos. A stochastic realization and model reduction approach to streamflow modeling, Ph. D. dissertation, Georgia Institute of Technology, Atlanta, Georgia, 1985.
E. I. Verriest. “Projection techniques for model reduction, MTNS-1985, Stockholm, Sweeden.
K.V. M. Fernando and H. Nicholson. “Discrete double sided Karhunen-Loeve expansion, IEE Proc. Vol. 127, Pt. D, No. 4, pp. 155–160, July 1980.
P. Robert and Y. Escoufier. “A unifying tool for linear multivariate statistical methods.: the RV-coefficient,” Appl. Stat., C, 25 (3), 257–265, 1976.
G. H. Golub and C. F. Van Loan, “Matrix computations, John Hopkins University Press, Baltimore, MD, 1983.
D. G. Kabe. “On some multivariate statistical methodology with applications to statistics, psychology, and mathematical programming,” The Journal of Industrial Mathematics, Vol. 35, pt. 1, pp. 1–18, 1985.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Ramos, J.A., Verriest, E.I. (1990). Canonical Variate Modeling and Approximation of Linear Systems. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Realization and Modelling in System Theory. Progress in Systems and Control Theory, vol 3. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3462-3_45
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3462-3_45
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8033-0
Online ISBN: 978-1-4612-3462-3
eBook Packages: Springer Book Archive