Stabilization of two-dimensional linear systems by Gaussian noise

• Autorzy: Bobryk, R. , Stettner, Ł.
• Języki publikacji: EN

Abstrakty

EN

In the paper a necessary and sufficient condition for the mean square stabilization of two-dimensional linear systems is obtained.

Słowa kluczowe

PL

procesy stochastyczne; teoria prawdopodobieństwa; układ liniowy

EN

Gaussian noise; linear systems; mean square stabilization

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no 1
• Strony: 91-103
• Opis fizyczny: Bibliogr. 11 poz.,

Twórcy

autor

Bobryk, R.

• Institute of Mathematics, Pedagogical University, M. Konopnickiej 15, 25-406 Kielce, Poland
• Institute For Applied Problem Of Mechanics And Mathematics, Urainian Academy of Sciences, Lviv, Ukraine (Rb)

autor

Stettner, Ł.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland, also Warsaw School of Managament and Marketing

Bibliografia

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• [2] F. Kozin, A survey of stability of stochastic systems, Automatica, 5 (1969) 95-112.
• [3] R. Z. Khasmiskii, Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, Alphen 1980.
• [4] L. L. Willems, D. Aeyels, An equivalence result for moment stability criteria for parametric stochastic systems and Itô equations, Intern. J. Systems Sci., 7 (1976) 577-590.
• [5] L. Arnold, P. Kloeden, Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise, SIAM J. Appi. Matki., 49 (1989) 1241-1274.
• [6] L. Arnold, H. Crauel, V. Wihsthutz, Stabilization of linear systems by noise, SIAM J. Contr. Optim., 21 (1983) 451-561.
• [7] G. C. Papanicolaou, W. Kohler, Asymptotic theory of mixing stochastic ordinary differential equations, Comm. Рurе Appl. Math., 27 (1974) 641-668.
• [8] V. Volterrа, Thеогy of Functionals and of Integral and Integro-Differential Equations, Dover Publ, New York 1959.
• [9] V. I. Averbuh, O. G. Smoljanov, Differention theory in linear topological spaces, Uspehi Mat. Nauk, 22 (1967) 201-260 (in Russian).
• [10] M. Donsker, On function sрасе integrals, in: Proc. Conf. Theory and Appl. Analysis in Funct. Space, MTI Press, Cambridge (1964) 17-30.
• [11] H. Cramer, M. R. Leadbetter, Stationary and Related Stochastic Processes, Wiley, New York 1967.