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Section
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Mathematics
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Title
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Necessary and sufficient conditions of the subcriticality for linear control systems
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Author(-s)
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Lukyanov V.V.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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linear control systems, subcritical systems, conditions of subcriticality
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UDC
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517.977
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MSC
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34H05
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DOI
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10.20537/vm130410
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Received
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30 October 2013
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Language
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Russian
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Citation
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Lukyanov V.V. Necessary and sufficient conditions of the subcriticality for linear control systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 100-108.
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References
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- Lukyanov V.V. Two-dimensional T-systems of functions and their application for research of time optimal linear nonstationary control systems, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 1, pp. 101-130.
- Nikolaev S.F., Tonkov E.L. The structure of the controllability set of a linear subcritical system, Differ. Uravn., 1999, vol. 35, no. 1, pp. 107-115.
- Krasovskii N.N. Teoriya upravleniya dvizheniem (Theory of motion control), Moscow: Nauka, 1968, 476 p.
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Full text
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