Canonical Variate Modeling and Approximation of Linear Systems

  • J. A. Ramos
  • E. I. Verriest
Part of the Progress in Systems and Control Theory book series (PSCT, volume 3)


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.


Singular Value Decomposition Canonical Variate Canonical Variate Analysis Hankel Matrix Balance Realization 
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  1. [1]
    F. Cailliez and J. P. Pages. “Introduction a l’analyse des données, Smash, Paris, 1976.Google Scholar
  2. [2]
    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.Google Scholar
  3. [3]
    J. A. Ramos and E. I. Verriest. “A unifying tool for comparing stochastic realization algorithms and model reduction techniques, Proc. 1984 ACC.Google Scholar
  4. [4]
    J. A. Ramos. A stochastic realization and model reduction approach to streamflow modeling, Ph. D. dissertation, Georgia Institute of Technology, Atlanta, Georgia, 1985.Google Scholar
  5. [5]
    E. I. Verriest. “Projection techniques for model reduction, MTNS-1985, Stockholm, Sweeden.Google Scholar
  6. [6]
    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.Google Scholar
  7. [7]
    P. Robert and Y. Escoufier. “A unifying tool for linear multivariate statistical methods.: the RV-coefficient,” Appl. Stat., C, 25 (3), 257–265, 1976.CrossRefGoogle Scholar
  8. [8]
    G. H. Golub and C. F. Van Loan, “Matrix computations, John Hopkins University Press, Baltimore, MD, 1983.Google Scholar
  9. [9]
    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.Google Scholar

Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • J. A. Ramos
  • E. I. Verriest

There are no affiliations available

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