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dc.contributor.author | Adukov, V. M. | |
dc.contributor.author | Fadeeva, A. S. | |
dc.contributor.author | Адуков, В. М. | |
dc.contributor.author | Фадеева, А. С. | |
dc.date.accessioned | 2015-09-28T08:43:04Z | |
dc.date.available | 2015-09-28T08:43:04Z | |
dc.date.issued | 2014 | |
dc.identifier.citation | Adukov, V. M. Solving of a minimal realization problem in Maple / V. M. Adukov, A.S. Fadeeva // Вестник ЮУрГУ. Серия Математическое моделирование и программирование.- 2014.- Т. 7. № 4.- С. 76-89.- Библиогр.: с. 87 (10 назв.) | ru_RU |
dc.identifier.issn | 2071-0216 | |
dc.identifier.uri | http://dspace.susu.ac.ru/xmlui/handle/0001.74/5285 | |
dc.description | V.M. Adukov, South Ural State University, Chelyabinsk, Russian Federation, adukovvm@susu.ac.ru,A.S. Fadeeva South Ural State University, Chelyabinsk, Russian Federation,fadeevaas@susu.ac.ru Адуков Виктор Михайлович, доктор физико-математических наук, кафедра дифференциальных уравнений и динамических систем, Южно-Уральский государственный университет, avm@susu.ac.ru. | ru_RU |
dc.description.abstract | In the computer algebra system Maple, we have created a package MinimalRealization to solve the minimal realization problem for a discrete-time linear time-invariant system. The package enables to construct the minimal realization of a system starting with either a nite sequence of Markov parameters of a system, or a transfer function, or any non-minimal realization. It is designed as a user library and consists of 11 procedures: ApproxEssPoly, ApproxNullSpace, Approxrank, ExactEssPoly, Fractional-FactorizationG, FractionalFactorizationMP, MarkovParameters, MinimalityTest, MinimalRealizationG, MinimalRealizationMP, Realization2MinimalRealization. The realization algorithm is based on solving of sequential problems: (1) determination of indices and essential polynimials (procedures ExactEssPoly, ApproxEssPoly), (2) construction of a right fractional factorization of the transfer function (FractionalFactorizationG, FractionalFactorizationMP), (3) construction of the minimal realization by the given fractional factorization (MinimalRealizationG, MinimalRealizationMP, Realization2MinimalRealization). We can solve the problem both in the case of exact calculations (in rational arithmetic) and in the presence of rounding errors, or for input data which are disturbed by noise. In the latter case the problem is ill-posed because it requires nding the rank and the null space of a matrix. We use the singular value decomposition as the most accurate method for calculation of the numerical rank (Approxrank) and the numerical null space (ApproxNullSpace). Numerical experiments with the package MinimalRealization demonstrate good agreement between the exact and approximate solutions of the problem. | ru_RU |
dc.language.iso | other | ru_RU |
dc.publisher | Издательский центр ЮУрГУ | ru_RU |
dc.relation.isformatof | Вестник ЮУрГУ. Серия Математическое моделирование и программирование | ru_RU |
dc.relation.isformatof | Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe modelirovanie i programmirovanie | ru_RU |
dc.relation.isformatof | Bulletin of SUSU | ru_RU |
dc.relation.ispartofseries | Математическое моделирование и программирование;Том 7 | |
dc.subject | discrete-time linear time-invariant systems | ru_RU |
dc.subject | fractional factorization | ru_RU |
dc.subject | minimal realization | ru_RU |
dc.subject | algorithms for solving of realization problem | ru_RU |
dc.subject | дискретная линейная конечномерная динамическая система | ru_RU |
dc.subject | дробная факторизация | ru_RU |
dc.subject | минимальная реализация | ru_RU |
dc.subject | алгоритмы решения задачи реализации | ru_RU |
dc.subject | УДК 519.71 | ru_RU |
dc.subject | УДК 004.4 | ru_RU |
dc.subject | ГРНТИ 50.05 | ru_RU |
dc.title | Solving of a minimal realization problem in Maple | ru_RU |
dc.title.alternative | Решение задачи минимальной реализации в системе Maple | ru_RU |
dc.type | Article | ru_RU |