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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.

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

Bibliographic databases:

UDC: 517.9
Received: 16.06.1975

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}


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