Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 25-40
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A. F. Gabdrahimov; V. A. Zaitsev. Lyapunov reducibility for four-dimensional linear stationary control systems in the class of the piecewise-constant control functions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 25-40. http://geodesic.mathdoc.fr/item/VUU_2006_1_a2/
@article{VUU_2006_1_a2,
author = {A. F. Gabdrahimov and V. A. Zaitsev},
title = {Lyapunov reducibility for four-dimensional linear stationary control systems in the class of the piecewise-constant control functions},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {25--40},
year = {2006},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2006_1_a2/}
}
TY - JOUR
AU - A. F. Gabdrahimov
AU - V. A. Zaitsev
TI - Lyapunov reducibility for four-dimensional linear stationary control systems in the class of the piecewise-constant control functions
JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY - 2006
SP - 25
EP - 40
IS - 1
UR - http://geodesic.mathdoc.fr/item/VUU_2006_1_a2/
LA - ru
ID - VUU_2006_1_a2
ER -
%0 Journal Article
%A A. F. Gabdrahimov
%A V. A. Zaitsev
%T Lyapunov reducibility for four-dimensional linear stationary control systems in the class of the piecewise-constant control functions
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2006
%P 25-40
%N 1
%U http://geodesic.mathdoc.fr/item/VUU_2006_1_a2/
%G ru
%F VUU_2006_1_a2
It is proved that if the stationary control system $\dot x=Ax+Bu,$$x\in\mathbb R^4,$$u\in\mathbb R^m$ is totally controllable, then for any constant matrix $C$ there exists bounded piecewise-constant matrix $U=U(t)$ such that the matrices $A+BU(t)$ and $C$ are kinematically similar. The constructed control function $U$ is locally bounded with respect to $C$.
