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Section
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Mathematics
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Title
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The space of linear control systems and its canonical representatives
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Author(-s)
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Tonkov E.L.a
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Affiliations
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Udmurt State Universitya
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Abstract
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The space of linear control systems that are parameterized with the help of a topological dynamical system is considered. For each invariant space (with respect to a flow in the dynamical system phase space) there are constructed its extension and the corresponding Perron transformation that reduces a given family of systems to the so-called canonical system. It is also proved that for minimal invariant spaces the Perron transformation possesses the recurrence property.
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Keywords
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linear control systems, controllability space, the Perron transformation, dynamical systems
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UDC
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517.917
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MSC
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34D08, 93С15
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DOI
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10.20537/vm120107
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Received
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1 February 2012
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Language
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Russian
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Citation
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Tonkov E.L. The space of linear control systems and its canonical representatives, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 60-76.
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References
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- Perron О. Uber line Matrixtransformation, Math. Z., 1930, no. 32, pp. 465–473.
- Millionshchikov V.M. The connection between the stability of characterisitic exponents and almost reducibility of linear systems of differential equations with almost periodic coefficients, Differ. Uravn., 1967, vol. 3, no. 12, pp. 2127–2134.
- Popova S.N., Tonkov E.L. Consistent systems and control over Lyapunov exponents, Differ. Uravn., 1997, vol. 33, no. 2, pp. 226–235.
- Tonkov E.L. Canonical representative of linear control system, Vestn. Udmurt. Univ. Mat., 2003, no. 1, pp. 113–123.
- Anosov D.V. Lektsii po lineinoi algebre (Lectures on linear algebra), Moscow: Regular and Chaotic Dynamics, 1999. 105 p.
- Anosov D.V., Aranson S.Kh., Arnol’d V.I., Bronshtein I.U., Grines V.Z., Il’yashenko Yu.S. Dynamical Systems–1, Itogi Nauki i Tekhniki Ser. Sovrem. Probl. Mat. Fund. Naprav., vol. 1, Moscow: Vseross. Inst. Nauchn. i Tekhn. Inform. (VINITI), 1985, 244 p.
- Nemytskii V.V., Stepanov V.V. Kachestvennaya teoriya differentsial’nykh uravnenii (Qualitative theory of differential equations), Moscow: GITTL, 1949. 550 p.
- Birkhoff G.D. Dynamical Systems, New York, 1927. Translated under the title Dinamicheskie sistemy, Izhevsk: RCD, 1999. 408 p.
- Bebutov M.V. Dynamical systems in the space of continuous function, Bull. Mat. Inst. Moscow State University, 1940, vol. 2, no. 5, pp. 1–52.
- Kalman R., Falb P., Arbib M. Topics in mathematical system theory, New York: McGraw-Hill, 1969, 358 p. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Editorial URSS, 2004, 400 p.
- Horn R., Johnson C. Matrix Analysis, Cambridge University Press, 1985. Translated under the title Matrichnyi analiz, Moscow: Mir, 1989, 655 p.
- Krasovskii N.N. Teoriya upravleniya dvizheniem (Theory of control of motion), Moscow: Nauka, 1968, 475 p.
- Tonkov E.L. Globally controllable linear systems, Sovrem. Mat. Prilozh., 2005, vol. 23, p. 145–165.
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