Geodesic
Singular sets and dynamic properties of bilinear control systems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 8, pp. 105-117.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with qualitative methods of investigation of dynamic systems with control. Classification of singular sets of two-dimensional bilinear control systems is proposed. Constructive criteria of presence of different kinds of singular sets in the phase portrait are obtained. Dependence of dynamic properties of systems such as oscillation, stability, instability, and controllability on the types of singular sets is investigated. Analytical conditions under which analysis of above properties is relatively simple are obtained. 
@article{FPM_2005_11_8_a4,
     author = {V. N. Zhermolenko},
     title = {Singular sets and dynamic properties of bilinear control systems},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {105--117},
     publisher = {mathdoc},
     volume = {11},
     number = {8},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a4/}
}
TY  - JOUR
AU  - V. N. Zhermolenko
TI  - Singular sets and dynamic properties of bilinear control systems
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 105
EP  - 117
VL  - 11
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a4/
LA  - ru
ID  - FPM_2005_11_8_a4
ER  - 
%0 Journal Article
%A V. N. Zhermolenko
%T Singular sets and dynamic properties of bilinear control systems
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 105-117
%V 11
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a4/
%G ru
%F FPM_2005_11_8_a4
V. N. Zhermolenko. Singular sets and dynamic properties of bilinear control systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 8, pp. 105-117. http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a4/

[1] Babichev A. V., Butkovskii A. G., Lepe N. L., “Osobye mnozhestva na fazovykh portretakh dinamicheskikh sistem s upravleniem. I, II”, Avtomatika i telemekhanika, 1986, no. 5, 24–31 ; No 7, 48–54 | MR | Zbl | MR | Zbl

[2] Butkovskii A. G., Fazovye portrety upravlyaemykh dinamicheskikh sistem, Nauka, M., 1985 | MR | Zbl

[3] Gabasov R., Kirillova F. M., Osobye optimalnye upravleniya, Nauka, M., 1973 | MR

[4] Zhermolenko V. N., “Kolebatelnost dvumernykh bilineinykh sistem”, Avtomatika i telemekhanika, 2005 (to appear)

[5] Molchanov A. P., Pyatnitskii E. S., “Funktsii Lyapunova, opredelyayuschie neobkhodimye i dostatochnye usloviya absolyutnoi ustoichivosti nelineinykh nestatsionarnykh sistem. II”, Avtomatika i telemekhanika, 1986, no. 4, 5–14 | MR

[6] Filippov A. F., “Usloviya ustoichivosti odnorodnykh sistem s proizvolnymi pereklyucheniyami rezhimov”, Avtomatika i telemekhanika, 1980, no. 8, 48–55 | MR | Zbl