Geodesic
Necessary and sufficient conditions of the subcriticality for linear control systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 100-108

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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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     author = {V. V. Lukyanov},
     title = {Necessary and sufficient conditions of the subcriticality for linear control systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {100--108},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_4_a9/}
}
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V. V. Lukyanov. Necessary and sufficient conditions of the subcriticality for linear control systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 100-108. http://geodesic.mathdoc.fr/item/VUU_2013_4_a9/