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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1978, Volume 23, Issue 2, Pages 253–259 (Mi mz8139)

The controllability of the equation $\dot x=ux$

Yu. M. Semenov

Chuvash State University

Abstract: The equation $\dot x=ux$, where $x\in R^n$ and $u\in G\subset M_n$ ($M_n$ is the ring of all $n\times n$ real matrices), is considered. The equation is called weakly controllable if for arbitrary points $a,b\in R^n$ these exist points $a'$ and $b'$ as near to $a$ and $b$, respectively, as we like and a control transforming $a'$ into $b'$. In this note algebraic criteria are given for the complete and the weak controllability of such equations in the case where the limiting set $G$ is closed with respect to the operation of matrix multiplication and the $G$-module $R^n$ is semisimple.

Full text: PDF file (633 kB)

English version:
Mathematical Notes, 1978, 23:2, 138–141

Bibliographic databases:

UDC: 517.9

Citation: Yu. M. Semenov, “The controllability of the equation $\dot x=ux$”, Mat. Zametki, 23:2 (1978), 253–259; Math. Notes, 23:2 (1978), 138–141

Citation in format AMSBIB
\Bibitem{Sem78} \by Yu.~M.~Semenov \paper The controllability of the equation $\dot x=ux$ \jour Mat. Zametki \yr 1978 \vol 23 \issue 2 \pages 253--259 \mathnet{http://mi.mathnet.ru/mz8139} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=504105} \zmath{https://zbmath.org/?q=an:0404.93007|0384.93008} \transl \jour Math. Notes \yr 1978 \vol 23 \issue 2 \pages 138--141 \crossref{https://doi.org/10.1007/BF01153155}