This work was partially supported by the Consiglio Nazionale delle Ricerche under Grant CNR-79.00700.01.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
M. Pavon, The conjugate process in stochastic realization theory, Mathematical Programming Study (forthcoming).
F. Badawi, A. Lindquist and M. Pavon, A stochastic realization approach to the smoothing problem, IEEE Trans. Aut. Control AC-24 (1979), pp.878–888.
A. Lindquist and G. Picci, On the stochastic realization problem, SIAM J. Contr. Optimiz. 17 (1979), pp.365–389.
—, Realization theory for multivariate stationary Gaussian processes, to be submitted.
A. Lindquist, G. Picci and G. Ruckebusch, On minimal splitting subspaces and Markovian representations, Math. Systems Theory 12 (1979), pp.271–279.
M. Pavon, Stochastic realization and invariant directions of the matrix Riccati equation, SIAM J. Contr. Optimiz. 18 (1980), pp. 155–180.
G. Ruckebusch, Representations markoviennes de processus Gaussien stationnaires, Thèse 3ème cycle, Univ. de Paris VI, May 1975.
—, Theorie géometrique de la représentation Markovienne, Thèse de Doctorat d'Etat, Univ. de Paris VI, April 1980.
J.C. Willems and J.H. Van Schuppen, Stochastic systems and the problem of state space realization, Stichting Matematisch Centrum, Report BW 108/79, Amsterdam, The Netherlands, June 1979.
Y.A. Rozanov, Stationary Random Processes, Holden-Day, San Francis co, 1967.
P. Masani, The prediction theory of multivariable stochastic processes, III, Acta Math. 104 (1960), pp.141–162.
J. Neveu, Processus Aléatoires Gaussiens, Presses de l'Université de Montréal, 1968.
B. Noble, Applied linear algebra, Prentice-Hall, Englewood Cliffs, 1969.
R.T. Rockafellar, Conjugate duality and optimization, SIAM Monograph Series, 1974.
R.T. Rockafellar, Integrals which are convex functionals, Pacific. J. Math., 24 (1968), 525–539.
I.C. Gohberg and M.G. Krein, Theory and applications of Volterra operators in Hilbert space, Amer. Math. Soc. Transl. 24, Providence, 1970.
R.M. De Santis, Stochastic optimal control and a separation theorem in Hilbert resolution space, Proc. Fourth Intern. Symposium on Math. Theory of Networks and Systems, Delft, The Netherlands, July 1979.
A. Feintuch, The causal invertibility problem, Proc. Fourth Intern. Symposium on Math. Theory of Networks and Systems, Delft, The Netherlands, July 1979.
R. Saeks, The factorization problem. A survey, IEEE Proc. 64 (1976) pp. 90–95.
A. Schumitzky, State feedback control for general linear systems, Proc. Fourth Intern. Symposium on Math. Theory of Networks and Systems, Delft, The Netherlands, July 1979.
A.V. Balakrishnan, Stochastic differential systems I, Lecture Notes in Economic and Mathematical Systems, vol.84, Springer-Verlag, Berlin, 1973.
P. Faurre, M. Clerget and F. Germain, Operateurs Rationnels Positifs, Dunod, Paris, 1979.
R. Geesey, Canonical representations of second order processes with applications, Technical Report n.7050-17, Systems Theory Laboratory, Stanford University, Stanford, California, June 1969.
E.A. Jonckheere and L.M. Silverman, Spectral theory of linear control and estimation problems, Proc. Intern. Symposium on Systems Optimization and Analysis, Rocquencourt, France, Dec. 1978.
T. Kailath, Application of a resolvent identity to a linear smoothing problem, SIAM J. Control 7 (1969), pp.68–74.
—, Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations, IEEE Inf. Theory IT-15 (1969), pp.665–672.
—, A note on least squares estimation by the innovations method, SIAM J. Control 10 (1972), pp.477–486.
—, Likelihood ratios for Gaussian processes, IEEE Inf. Theory IT-16 (1970), pp.276–288.
—, A view of three decades of linear filtering theory, IEEE Trans. Inf. Theory IT-20 (1974), pp.146–181.
T. Kailath, B. Lévy, L. Ljung and M. Morf, The factorization and representation of operators in the algebra generated by Toeplitz operators, SIAM J. Appl. Math. 37 (1979), pp.467–484.
G. Kallianpur, Non-anticipative canonical representations of equivalent Gaussian processes, Multivariate Analysis, vol. 3, P.R. Krishnaiah Ed., Academic Press, New York, 1973, pp.31–44.
A. Lindquist, Optimal control of linear stochastic systems with applications to time lag systems, Information Sciences 5 (1973), pp.81–126.
—, On Fredholm integral equations, Toeplitz equations and Kalman-Bucy filtering, Appl. Math. Optimiz. 1 (1975), pp.355–373.
Y.A. Rozanov, Innovation processes, Wiley, New York, 1977.
N. Wiener and P. Masani, The prediction theory of multivariable stochastic processes I and II, Acta Math. 98 (1957), pp.111–150 and 99 (1958), pp.93–137.
M.H.A. Davis, A direct proof of innovations/observations equivalence for Gaussian processes, IEEE Trans. Inf. Theory IT-24 (1978), pp.252–254.
I.I. Gikman and A.V. Skorokhod, Introduction to the Theory of Random Processes, Saunders, Philadelphia, 1969.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Veralg
About this paper
Cite this paper
Pavon, M. (1980). On the Gohberg-Kerin factorization and the conjugate process. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004048
Download citation
DOI: https://doi.org/10.1007/BFb0004048
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10472-8
Online ISBN: 978-3-540-38489-2
eBook Packages: Springer Book Archive