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2015 | OriginalPaper | Chapter

7. The Geometry of Splitting Subspaces

Authors : Anders Lindquist, Giorgio Picci

Published in: Linear Stochastic Systems

Publisher: Springer Berlin Heidelberg

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Abstract

The purpose of this chapter is to introduce coordinate-free representations of a stationary process y by constructing state spaces from basic principles. This will in particular accommodate both finite- and infinite-dimensional stochastic systems.

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previous chapter Linear Finite-Dimensional Stochastic Systems
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Literature
6.
51.
Caines, P.E., Delchamps, D.: Splitting subspaces, spectral factorization and the positive real equation: structural features of the stochastic realization problem. In: Proceedings of the 19th IEEE Conference on Decision and Control, Albuquerque, pp. 358–362 (1980)
163.
Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory. McGraw-Hill, New York (1969)MATH
180.
Lax, P.D., Phillips, R.S.: Scattering Theory. Volume 26 of Pure and Applied Mathematics, 2nd edn. Academic, Boston (1989). With appendices by Cathleen S. Morawetz and Georg Schmidt
191.
Lindquist, A., Michaletzky, G.: Output-induced subspaces, invariant directions and interpolation in linear discrete-time stochastic systems. SIAM J. Control Optim. 35, 810–859 (1997)CrossRefMATHMathSciNet
192.
Lindquist, A., Michaletzky, Gy., Picci, G.: Zeros of spectral factors, the geometry of splitting subspaces, and the algebraic Riccati inequality. SIAM J. Control Optim. 33(2), 365–401 (1995)
195.
Lindquist, A., Picci, G.: On the structure of minimal splitting subspaces in stochastic realization theory. In: Proceedings of the 1977 IEEE Conference on Decision and Control, New Orleans, 1977, vol. 1, pp. 42–48. IEEE, New York (1977)
197.
Lindquist, A., Picci, G.: A state-space theory for stationary stochastic processes. In: Proceedings of the 21st Midwestern Symposium on Circuits and Systems, Ames, 1978, pp. 108–113 (1978)
199.
Lindquist, A., Picci, G.: Realization theory for multivariate Gaussian processes I: state space construction. In: Proceedings of the 4th International Symposium on the Mathematical Theory of Networks and Systems, Delft, 1979, pp. 140–148 (1979)
200.
Lindquist, A., Picci, G.: Realization theory for multivariate Gaussian processes: II: state space theory revisited and dynamical representations of finite-dimensional state spaces. In: Second International Conference on Information Sciences and Systems, University of Patras, Patras, 1979, vol. II, pp. 108–129. Reidel, Dordrecht (1980)
205.
Lindquist, A., Picci, G.: Realization theory for multivariate stationary Gaussian processes. SIAM J. Control Optim. 23(6), 809–857 (1985)CrossRefMATHMathSciNet
206.
Lindquist, A., Picci, G.: A geometric approach to modelling and estimation of linear stochastic systems. J. Math. Syst. Estim. Control 1(3), 241–333 (1991)MathSciNet
210.
Lindquist, A., Picci, G., Ruckebusch, G.: On minimal splitting subspaces and Markovian representations. Math. Syst. Theory 12(3), 271–279 (1979)MATHMathSciNet
248.
Picci, G.: Stochastic realization of Gaussian processes. Proc. IEEE 64(1), 112–122 (1976). Recent trends in system theory
273.
Ruckebusch, G.: Représentations markoviennes de processus guassiens startionaires. C. R. Acad. Sc. Paris Ser. A 282, 649–651 (1976)MATH
275.
Ruckebusch, G.: On the theory of Markovian representation. In: Measure Theory Applications to Stochastic Analysis. Proceedings of the Conference on Mathematical Research Institute, Oberwolfach, 1977. Volume 695 of Lecture Notes in Mathematics, pp. 77–87. Springer, Berlin (1978)
276.
Ruckebusch, G.: A state space approach to the stochastic realization problem. In: Proceedings of the 1978 International Symposium on Circuits and Systems, New York (1978)
277.
Ruckebusch, G.: Théorie géométrique de la représentation markovienne. Ann. Inst. H. Poincaré Sect. B (N.S.) 16(3), 225–297 (1980)
319.
Yosida, K.: Functional Analysis. Volume 123 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 6th edn. Springer, Berlin (1980)
Metadata
Title
The Geometry of Splitting Subspaces
Authors
Anders Lindquist
Giorgio Picci
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
Book
Linear Stochastic Systems

Print ISBN: 978-3-662-45749-8

Electronic ISBN: 978-3-662-45750-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-662-45750-4_7