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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.
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
Linking options:
https://www.mathnet.ru/eng/mzm8139 https://www.mathnet.ru/eng/mzm/v23/i2/p253
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Abstract page: | 189 | Full-text PDF : | 73 | First page: | 1 |
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