Section
|
Mathematics
|
Title
|
Necessary and sufficient conditions of the subcriticality for linear control systems
|
Author(-s)
|
Lukyanov V.V.a
|
Affiliations
|
Udmurt State Universitya
|
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
|
UDC
|
517.977
|
MSC
|
34H05
|
DOI
|
10.20537/vm130410
|
Received
|
30 October 2013
|
Language
|
Russian
|
Citation
|
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.
|
References
|
- 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.
|
Full text
|
|