Geodesic
Sufficient conditions for the local controllability of systems with random parameters for an arbitrary number of states of a system
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2008), pp. 38-49.

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We obtain sufficient conditions for the existence of a nonanticipating control for linear systems with stationary random parameters. We consider the case of a bounded control and an arbitrary number of system states. We estimate the probability that the system is nonanticipatingly locally controllable on a fixed time interval. We formulate the main assertions in terms of Lyapunov functions, choosing the latter in the class of piecewise continuously differentiable functions.
Keywords: control systems, local controllability, Lyapunov functions, nonanticipating control. 
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     title = {Sufficient conditions for the local controllability of systems with random parameters for an arbitrary number of states of a system},
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Yu. V. Masterkov; L. I. Rodina. Sufficient conditions for the local controllability of systems with random parameters for an arbitrary number of states of a system. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2008), pp. 38-49. http://geodesic.mathdoc.fr/item/IVM_2008_3_a3/

[1] Khasminsky R. Z., “Limit theorem for a solution of the differential equation with a random right part”, Prob. Theor. Appl., 11:3 (1966), 444–462 | MR

[2] Baranova O. V., “O ravnomernoi globalnoi upravlyaemosti lineinoi sistemy so statsionarnymi sluchainymi parametrami”, Differents. uravneniya, 27:11 (1991), 1843–1850 | MR | Zbl

[3] Colonius F., Jonson R., “Local and global null controllability of time varying linear control systems”, Control, Optimization and Calculus of Variations, V. 2 (November 1997), 329–341 | Zbl

[4] De Farias D. P., Geromel J. C., Do Val J. B. R., Costa O. L. V., “Output feedback control of Markov jump linear systems in continuous-time”, IEEE Trans. Autom. Contr., 45:5 (2000), 944–949 | DOI | MR | Zbl

[5] Tsarkov Ye., “Asymptotic methods for stability analysis of Markov impulse dynamical systems”, Nonlin. Dynam. Syst. Theor., 2:1 (2002), 103–115 | MR | Zbl

[6] Ibrir S., Boukas E. K., “A constant-gain nonlinear estimator for linear switching systems”, Nonlin. Dynam. Syst. Theor., 5:1 (2005), 49–59 | MR | Zbl

[7] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 286 pp. | MR

[8] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 520 pp. | MR

[9] Nikolaev S. F., Tonkov E. L., “Differentsiruemost vektora bystrodeistviya i pozitsionnoe upravlenie lineinoi dokriticheskoi sistemoi”, Differents. uravneniya, 36:1 (2000), 76–84 | MR | Zbl

[10] Nikolaev S. F., Tonkov E. L., “O nekotorykh zadachakh, svyazannykh s suschestvovaniem i postroeniem neuprezhdayuschego upravleniya dlya nestatsionarnykh upravlyaemykh sistem”, Vestn. Udmurtsk. un-ta, 2000, no. 1, 11–32

[11] Masterkov Yu. V., Rodina L. I., “Upravlyaemost lineinoi dinamicheskoi sistemy so sluchainymi parametrami”, Differents. uravneniya, 43:4 (2007), 457–464 | MR | Zbl

[12] Masterkov Yu. V., Rodina L. I., “O postroenii neuprezhdayuschego upravleniya dlya sistem so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta, 2005, no. 1, 101–114

[13] Masterkov Yu. V., Rodina L. I., “Usloviya lokalnoi upravlyaemosti sistem so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta, 2006, no. 1, 81–94

[14] Masterkov Yu. V., Rodina L. I., “The sufficient conditions of local controllability for linear systems with random parameters”, Nonlin. Dynam. Syst. Theor., 7:3 (2007), 303–314 | MR | Zbl

[15] Shiryaev A. N., Veroyatnost, Nauka, M., 1989, 640 pp.

[16] V. S. Korolyuk, N. I. Portenko, A. V. Skorokhod, A. F. Turbin (red.), Spravochnik po teorii veroyatnostei i matematicheskoi statistike, Nauka, M., 1985, 640 pp. | MR | Zbl

[17] Kornfeld I. P., Sinai Ya. G., Fomin S. V., Ergodicheskaya teoriya, Nauka, M., 1980, 383 pp. | MR

[18] Rozanov Yu. A., Statsionarnye sluchainye protsessy, Nauka, M., 1990, 272 pp. | MR

[19] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 476 pp. | MR

[20] Rodina L. I., Tonkov E. L., “Usloviya polnoi upravlyaemosti nestatsionarnoi lineinoi sistemy v kriticheskom sluchae”, Kibern. i sist. analiz, 40:3 (2004), 87–100 | MR | Zbl

[21] Galperin E. A., Krasovskii N. N., “O stabilizatsii statsionarnykh dvizhenii v nelineinykh upravlyaemykh sistemakh”, Prikl. matem. i mekh., 27 (1963), 1–24

[22] Roxin E., “Stability in general control systems”, J. Different. Equat., 1:2 (1965), 115–150 | DOI | MR | Zbl

[23] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985, 224 pp. | MR

[24] Galperin E. A., “Some generalization of Lyapunov's approach to stability and control”, Nonlin. Dynam. Syst. Theor., 2:1 (2002), 1–24 | MR

[25] Barbashin E. A., Funktsii Lyapunova, Nauka, M., 1970, 240 pp. | MR | Zbl