×

Controllability of linear stochastic systems. (English) Zbl 0493.93009


MSC:

93B05 Controllability
93C05 Linear systems in control theory
93E03 Stochastic systems in control theory (general)
Full Text: DOI

References:

[1] Arnold, L.; Kliemann, W., Qualitative theory of stochastic systems, (Bharucha-Reid, A. T., Probabilistic Analysis and Related Topics, Vol. 3 (1982), Academic Press: Academic Press New York) · Zbl 0536.60070
[2] Boyarski, A., Finite-dimensional attainable sets for stochastic control systems, J. Optim. Theory Appl., 22, 429-445 (1977) · Zbl 0336.93045
[3] Chen, H.-F., On stochastic observability, Scientia Sinica, 20, 305-323 (1977) · Zbl 0364.93042
[4] Chen, H.-F., On the stochastic observability and controllability, (Proceedings of the 7th IFAC World Congress (1978)), 1155-1162 · Zbl 0729.62082
[5] Çinlar, E.; Jacod, J.; Protter, P.; Sharpe, M. J., Semi-martingales and Markov processes, Z. Wahrsch. Verw. Gebiete, 54, 161-219 (1980) · Zbl 0443.60074
[6] Dym, H., Stationary measures for the flow of a linear differential equation driven by white noise, Trans. Amer. Math. Soc., 123, 130-164 (1966) · Zbl 0142.13701
[7] Dynkin, E. B., (Markov Processes 1 (1965), Springer: Springer Berlin) · Zbl 0132.37901
[8] Erickson, R. V., Constant coefficient linear differential equations driven by white noise, Ann. Math. Stat., 2, 820-823 (1971) · Zbl 0235.60057
[9] Godbole, S. S., Comments on “The maximally achievable accuracy of linear optimal regulators and linear optimal filters”, IEEE Trans. Automat. Control., 17, 577 (1972)
[10] Hasminskii, R. Z., Stochastic Stability of Differential Equations (1969), Sijthoff & Noordhoff: Sijthoff & Noordhoff Alphen aan den Rijn, 1980 translation from Russian · Zbl 0419.62037
[11] Kalman, R.; Arbib, M. A.; Falb, P. L., Topics in Mathematical Systems Theory (1969), McGraw-Hill: McGraw-Hill New York · Zbl 0231.49001
[12] Klamka, J.; Socha, L., Some remarks about stochastic controllability, IEEE Trans. Automat. Control., 22, 880-881 (1977) · Zbl 0363.93048
[13] Kwakernaak, H.; Sivan, R., The maximally achievable accuracy of linear optimal regulators and linear optimal filters, IEEE Trans. Automat. Control., 17, 79-86 (1972) · Zbl 0259.93057
[14] Miyahara, Y., Ultimate boundedness of systems governed by stochastic differential equations, Nagoya Math. J., 47, 111-144 (1972) · Zbl 0222.60036
[15] Sunahara, Y.; Kabeuchi, T.; Asada, Y.; Aihara, S.; Kishino, K., On stochastic controllability for nonlinear systems, IEEE Trans. Automat. Control, 19, 49-54 (1974) · Zbl 0276.93011
[16] Sunahara, Y.; Aihara, S.; Kishino, K., On the stochastic observability and controllability for non-linear systems, Int. J. Control, 22, 65-82 (1975) · Zbl 0315.93021
[17] Wonham, W. M., Linear Multivariable Control (1979), Springer: Springer New York · Zbl 0393.93024
[18] Zabczyk, J., Controllability of stochastic linear systems, Syst. Control. Lett., 1, 25-31 (1981) · Zbl 0481.93054
[19] Zabczyk, J., Controllability of Gaussian processes (1982), Preprint · Zbl 0502.93062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.