RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 3, Pages 38–55 (Mi timm405)  

This article is cited in 10 scientific papers (total in 10 papers)

Analysis of coordinate and other transformations of models of dynamical systems by the reduction method

S. N. Vassilyeva, R. I. Kozlovb, S. A. Ul'yanova

a Institute of Control Sciences, Russian Academy of Sciences
b Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: The issues of preserving dynamic properties when passing from a system of differential equations to another system obtained by a change of variables are considered, as well as issues of preserving the properties in the opposite direction. The possibilities of the reduction method, which was proposed earlier, in resolving these questions are demonstrated by the examples of such properties as stability, attraction, and dissipativity. Similar questions are investigated for the case when the second system is obtained by a way characteristic for the comparison method with vector Lyapunov functions. The application of one of the obtained dissipativity criteria to analyzing the nonlinear dynamics of a group of moving objects is considered.

Keywords: differential equations, stability, dissipativity, reduction method, coordinate transformations, vector Lyapunov functions, group control, formation stability.

Full text: PDF file (265 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 268, suppl. 1, S264–S282

Bibliographic databases:

Document Type: Article
UDC: 517+519
Received: 29.04.2009

Citation: S. N. Vassilyev, R. I. Kozlov, S. A. Ul'yanov, “Analysis of coordinate and other transformations of models of dynamical systems by the reduction method”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 38–55; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S264–S282

Citation in format AMSBIB
\Bibitem{VasKozUly09}
\by S.~N.~Vassilyev, R.~I.~Kozlov, S.~A.~Ul'yanov
\paper Analysis of coordinate and other transformations of models of dynamical systems by the reduction method
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 3
\pages 38--55
\mathnet{http://mi.mathnet.ru/timm405}
\elib{http://elibrary.ru/item.asp?id=12834731}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 268
\issue , suppl. 1
\pages S264--S282
\crossref{https://doi.org/10.1134/S0081543810050184}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000276615600018}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952250867}


Linking options:
  • http://mi.mathnet.ru/eng/timm405
  • http://mi.mathnet.ru/eng/timm/v15/i3/p38

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vassilyev S.N., Ul'yanov S.A., “Preservation of stability of dynamical systems under homomorphisms”, Differential Equations, 45:12 (2009), 1709–1720  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ya. I. Petrikevich, “Lineinye algoritmy upravleniya geometricheskim raspolozheniem ob'ektov v mnogoagentnoi sisteme”, UBS, 30.1 (2010), 665–680  mathnet
    3. Melnikov V.G., “Linearizatsiya v rasshirennom fazovom prostranstve nelineinykh polinomialnykh dinamicheskikh sistem”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1: Matematika. Mekhanika. Astronomiya, 2011, no. 3, 116–123  elib
    4. Melnikov V.G., “Preobrazovanie dinamicheskikh mnogochlennykh sistem s primeneniem approksimatsii chebysheva”, Nauchno-tekhnicheskii vestnik informatsionnykh tekhnologii, mekhaniki i optiki, 2012, 85–90  elib
    5. Vassilyev S.N., Kozlov R.I., Ul'yanov S.A., “Multimode Formation Stability”, Dokl. Math., 89:2 (2014), 257–262  crossref  mathscinet  zmath  isi  elib  scopus
    6. Melnikov V.G., Melnikov G.I., Malykh K.S., Dudarenko N.A., “Poincaré-Dulac Method With Chebyshev Economization in Autonomous Mechanical Systems Simulation Problem”, 2015 International Conference on Mechanics Seventh Polyakhovs Reading, ed. Tikhonov A., IEEE, 2015  mathscinet  isi
    7. Ul'yanov S.A., Maximkin N.N., “Stabilization of Multi-Auv Formation With Digital Control”, 2016 39Th International Convention on Information and Communication Technology, Electronics and Microelectronics (Mipro), eds. Biljanovic P., Butkovic Z., Skala K., Grbac T., CicinSain M., Sruk V., Ribaric S., Gros S., Vrdoljak, IEEE, 2016, 1108–1113  crossref  isi  scopus
    8. Ul'yanov S., Maksimkin N., “Software Toolbox For Analysis and Design of Nonlinear Control Systems and Its Application to Multi-Auv Path-Following Control”, 2017 40Th International Convention on Information and Communication Technology, Electronics and Microelectronics (Mipro), eds. Biljanovic P., Koricic M., Skala K., Grbac T., CicinSain M., Sruk V., Ribaric S., Gros S., Vrdoljak , IEEE, 2017, 1032–1037  crossref  isi  scopus
    9. Vassilyev S., Ulyanov S., Maksimkin N., “A Vlf-Based Technique in Applications to Digital Control of Nonlinear Hybrid Multirate Systems”, Icnpaa 2016 World Congress: 11Th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, AIP Conference Proceedings, 1798, ed. Sivasundaram S., Amer Inst Physics, 2017, UNSP 020170  crossref  isi  scopus
    10. Alyshev A.S., Dudarenko N.A., Melnikov V.G., Melnikov G.I., “The Use of Lyapunov Differential Inequalities For Estimating the Transients of Mechanical Systems”, Eighth Polyakhov'S Reading, AIP Conference Proceedings, 1959, eds. Kustova E., Leonov G., Morosov N., Yushkov M., Mekhonoshina M., Amer Inst Physics, 2018, UNSP 080007-1  crossref  isi  scopus
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:313
    Full text:90
    References:31
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019