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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 4, Pages 100–108 (Mi vuu405)

MATHEMATICS

Necessary and sufficient conditions of the subcriticality for linear control systems

V. V. Lukyanov

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: A linear control system with continuous coefficients is considered. We obtain a sufficient condition of the subcriticality for such system. The necessary condition of the subcriticality for a linear time-invariant system is obtained. The link between subcritical linear systems and completely controllable linear systems is studied. It is proved that a linear system is completely controllable on closed interval if the system is subcritical at some point in the interior of this interval. It is proved that a completely controllable linear time-invariant system with one-dimensional control is subcritical.

Keywords: linear control systems, subcritical systems, conditions of subcriticality.

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UDC: 517.977
MSC: 34H05

Citation: V. V. Lukyanov, “Necessary and sufficient conditions of the subcriticality for linear control systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4, 100–108

Citation in format AMSBIB
\Bibitem{Luk13} \by V.~V.~Lukyanov \paper Necessary and sufficient conditions of the subcriticality for linear control systems \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2013 \issue 4 \pages 100--108 \mathnet{http://mi.mathnet.ru/vuu405}