Abstract
The paper deals with balanced state space realizations and balanced forms. A structure theory treating the topological properties of the parametrization and the parameter space is developed. These results are important for identification. Finally balanced parametrizations are compared with parametrizations corresponding to Echelon forms.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
K.S.Arun, S.Y. Kung: Balanced Approximation of Stochastic Systems, SIAM J. Matrix Anal. Appl., Jan. 1990, Vol. 11, No. 1, p. 42–68
M.Aoki: State Space Modelling of Time Series, Springer-Verlag Berlin, 1987
D. Bauer: Strucutre of Balanced Realizations of Discrete Time State Space Systems, Master Thesis, TU Wien, 1994
A. S. Deif: Advanced Matrix Theory for Scientists and Engineers, Abacus Press, Gordon and Breach Science Publishers, 1991
U. B. Desai, D. Pal: A Transformation Approach to Stochastic Model Reduction, IEEE Transactions on Automatic Control, Dec. 1984, Vol. 29, p. 1097–1100
K. Glover: All Optimal Hankel-norm Approximations of Linear Multivariable Systems and Their L∞-error bounds, Int. J. Control, 1984, Vol. 39, No. 6, p. 1115–1193
E. J. Hannan, M. Deistler: The Statistical Theory of Linear Systems, Wiley Series, 1988
P. T. Kabamba: Balanced Forms: Canonicity and Parametrization, IEEE Transactions on Automatic Control, Nov. 1985, Vol. 30, p. 1106–1109
A. J. Laub, M. T. Heath, C. C. Paige, R. C. Ward: Computation of System Balancing Transformations and Other Applications of Simultaneous Diagonalization Algorithms, IEEE Transactions on Automatic Control, Feb. 1987, Vol. 32, No. 2, p. 115–121
J. M. Maciejowski: Balanced Realizations in System Identification, Proc. 7th IFAC Symposium on Identification and Parameter Estimation, York, U.K., 1985
B. P. McGinnie: A balanced view of System Identification, PhD Thesis, University of Cambridge, 1993
B.C.Moore: Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction, IEEE Transactions on Automatic Control, Feb. 1981, Vol. 26, p. 17–31
C. T. Mullis, R. A. Roberts: Synthesis of Minimum Roundoff Noise Fixed Point Digital Filters, IEEE Transactions on Circuits and Systems, Sept 1976, Vol. 23, No. 9, p. 551–561
R. Ober: Balanced Realizations: Canonical Forms, Parametrization, Model Reduction, Int. J. Control, 1987, Vol. 46, No. 2, p. 643–670
R. Ober: Balanced Parametrization of Classes of Linear Systems, SIAM J. Control and Optimization, Nov. 1991, Vol. 29, No. 6, p. 1251–1287
L. Pernebo, L. Silverman: Model Reduction Via Balanced State-Space Systems, IEEE Transactions on Automatic Control, April 1982, Vol. 27, p. 382–387
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Bauer, D., Deistler, M. (1996). Balanced Parametrizations: A Structure Theory for Identification. In: Robinson, P.M., Rosenblatt, M. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2412-9_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2412-9_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94787-7
Online ISBN: 978-1-4612-2412-9
eBook Packages: Springer Book Archive