Abstract
The transition from a given state space representation of a continuous-time, stochastic linear system to its minimal state, minimal estimator and minimal output representations is investigated. The analysis is centered about the minimal state predictor, which is shown to be the connecting link between the different representations. The role of minimal representation in feedback system design is also examined.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
E.G. Gilbert, “Controllability and Observability in Multivariable Control Systems”, SIAM J. Control, Vol. 1, No. 2, pp. 128–151, 1963.
R.E. Kalman, “Mathematical Description of Linear Dynamical Systems”, SIAM J. Control, Vol. 1, No. 2, pp. 152–192, 1963.
L.M. Silverman, “Realization of Linear Dynamical Systems”, IEEE Trans. on Automat. Contr. Vol. AC-16, No. 6, 1971.
N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series, The M.I.T. Press, 1949.
B.D.O. Anderson, “The Inverse Problem of Stationary Covariance Generation”, J. Statist. Phys. Vol. 1, pp. 133–147, 1969.
H. Akaike, “Markovian Representation of Stochastic Processes by Canonical Variables”, SIAM J. Control, Vol. 13, No. 1, 1975.
H. Akaike, “Stochastic Theory of Minimal Realization”, IEEE Trans. on Automatic Control, Vol. AC-19, pp. 716–723, 1974.
P.L. Faurre, “Stochastic Realization Algorithms”, in System Identification, R.K. Mehra and D.G. Lainiotis, Eds., New York, Academic Press, 1976.
G. Picci, “Stochastic Realization of Gaussian Processes”, Proc. IEEE, Vol. 64, Jan. 1976.
A. Lindquist and G. Picci, “On the Stochastic Realization Problem”, SIAM J. Contr. Optimiz., Vol. 17, May 1979.
A. Lindquist and G. Picci, “On the Structure of Minimal Splitting Subspaces in Stochastic Realization Theory”, Proc. CDC, New Orleans, Dec. 1977.
D.G. Luenberger, “An Introduction to Observers”, IEEE Trans. on Automat. Contr. Vol. AC-16, No. 6, 1971.
A.E. Bryson and D.E. Johansen, “Linear Filtering for Time Varying Systems Using Measurements Containing Colored Noise”, IEEE Trans. on Automat. Contr. Vol. AC-10, No. 1, 1965.
E. Tse and M. Athans, “Optimal Minimal Order Observer — Estimators for Discrete Linear Time — Varying Systems”, IEEE Trans. on Automat. Contr. Vol. AC-15, No. 4, 1970.
R.W. Brockett, Finite Dimensional Linear Systems, Wiley, 1970.
Y. Baram, Realization and Reduction of Markovian Models from Nonstationary Data”, IEEE Trans. on Automat. Contr. Vol. AC-26, No. 6, 1981.
T. Kailath, Linear Systems, Prentice-Hall, 1980.
A.E. Bryson, Jr. and Y-C Ho, Applied Optimal Control, Ginn and Company, 1969.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Baram, Y. (1984). Minimal order representation, estimation and feedback of continuous-time stochastic linear systems. In: Fuhrmann, P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031042
Download citation
DOI: https://doi.org/10.1007/BFb0031042
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13168-7
Online ISBN: 978-3-540-38826-5
eBook Packages: Springer Book Archive