Decomposition of discrete nonlinear systems with fast and slow variables
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2010), pp. 28-41 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to decomposition of nonlinear discrete multitempo systems. The algorithm of decomposition is based on geometric approach and properties of slow and fast manifolds. The separating transformation is constructed as asymptotic series.
Mots-clés : decomposition
Keywords: nonlinear discrete systems.
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N. V. Voropaeva. Decomposition of discrete nonlinear systems with fast and slow variables. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2010), pp. 28-41. http://geodesic.mathdoc.fr/item/VSGU_2010_4_a3/

[1] Naidu D. S., Price D. D., Hibey J. L., “Singular Perturbations and Time Scales (SPaTS) in Discrete Control Systems – an Overview”, Proc. 26-th IEEE Conf. on Decision and Control. Los Angeles, 1987, 2096–2103 | DOI

[2] Naidu D. S., “Singular Perturbations and Time Scales in Control Theory and Applications: an Overview”, Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications and Algorithms, 9:2 (2002), 233–278 | MR | Zbl

[3] Dmitriev M. G., Kurina G. A., “Singulyarnye vozmuscheniya v zadachakh upravleniya”, AiT, 2006, no. 1, 3–51 | MR | Zbl

[4] Sobolev V. A., “Integral manifolds and decomposition of singularly perturbed systems”, Syst. and Control Lett., 1984, no. 5, 169–279 | DOI | MR

[5] Voropaeva N. V., Sobolev V. A., Dekompozitsiya mnogotempovykh sistem, SMS, Samara, 2000, 290 pp.

[6] Voropaeva N. V., Sobolev V. A., Geometricheskaya dekompozitsiya singulyarno vozmuschennykh sistem, FIZMATLIT, M., 2009, 256 pp. | Zbl

[7] Voropaeva N. V., Sobolev V. A., “Dekompozitsiya raznotempovykh diskretnykh sistem upravleniya”, Mekhatronika, avtomatizatsiya, upravlenie, 2004, no. 8, 2–6

[8] Voropaeva N. V., Sobolev V. A., “Dekompozitsiya lineino-kvadratichnoi zadachi optimalnogo upravleniya s bystrymi i medlennymi peremennymi”, AiT, 2006, no. 8, 3–11 | MR | Zbl

[9] Voropaeva N. V., “Dekompozitsiya zadach optimalnogo upravleniya i otsenivaniya dlya diskretnykh sistem s bystrymi i medlennymi peremennymi”, AiT, 2008, no. 6, 15–25 | MR | Zbl

[10] Bobrovski D., Vvedenie v teoriyu dinamicheskikh sistem s diskretnym vremenem, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2006 | MR

[11] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, Mir, M., 1971 | MR