Stationary orbits of linear time-varying observation systems
https://doi.org/10.29235/1561-8323-2021-65-1-18-24
Abstract
In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.
About the Author
A. I. Astrovskii
Belarus State Economic Univesity
Belarus
Belarus
Astrovskii Anatoly I. – D. Sc. (Physics and Mathematics), Professor
26, Partizanskii Ave., 220070, Minsk
References
1. Lyapunov A. M. On general problem of stability motion. Moscow, GITTL Publ., 1950. 472 p. (in Russian).
2. Erugin N. P. Reducible systems. Vol. 13. Moscow, USSR Academy of Sciences Publishing House,1946. 96 p. (in Russian).
3. Bogdanov U. S., Chebotarev G. N. About commuting matrices with its derivative. Izvestiya vuzov. Matematika = Russian Mathematics, 1959, no. 4(11), pp. 27–37 (in Russian).
4. Bogdanov U. S. Asymptotic characteristic of solutions of linear differential systems. Trudy chetvertogo Vsesoyuznogo matematicheskogo s’ezda. Vol. 2 [Proceedings of the Fourth All-Union Mathematical Congress]. Leningrad, 1964, pp. 424–432 (in Russian).
5. Gaishun I. V. Introduction to the theory of linear nonstationary systems. Moscow, Editorial URSS Publ., 2004. 409 p. (in Russian).
6. Izobov N. A. Lyapunov Exponents and Stability. Cambridge, 2012. 353 p.
7. Makarov E. K., Popova S. N. Controllability of asymptotic invariants of time-varying linear systems. Minsk, Belaruskaya navuka Publ., 2012. 407 p. (in Russian).
8. Astrovskii A. I., Gaishun I. V. Linear systems with quasidifferential coefficients: controllability and observability of motion. Minsk, Belaruskaya navuka Publ., 2013. 213 p. (in Russian).
9. Astrovskii A. I., Gaishun I. V. State Estimation for Linear Time-Varying Observation Systems. Differential Equations, 2019, vol. 55, no. 3, pp. 363–373. https://doi.org/10.1134/s0012266119030108
10. Astrovskii A. I., Gaishun I. V. Observability of Linear Time-Varying Systems with Quasiderivative Coefficients. SIAM Journal on Control and Optimization, 2019, vol. 57, no. 3, pp. 1710–1729. https://doi.org/10.1137/18m1167115
11. Gaishun I. V., Astrovskii A. I. Description of the set of uniformly observable linear time-varying systems. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 1996, vol. 40, no. 5, pp. 5–8 (in Russian).
12. Morozov V. M., Kalenova V. I. Estimation and control of time-varying linear systems. Moscow, Moscow State University Publishing House, 1988. 144 p. (in Russian).
13. Kalenova V. I., Morozov V. M. The reducibility of linear second-order time-varying systems with control and observation. Journal of Applied Mathematics and Mechanics, 2012, vol. 76, no. 4, pp. 413–422. https://doi.org/10.1016/j.jappmathmech.2012.09.008
Review
Views: 552
Email this article 