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



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 9, Pages 57–70 (Mi ivm7128)  

This article is cited in 11 scientific papers (total in 11 papers)

The solvability of the initial problem for a degenerate linear hybrid system with variable coefficients

A. A. Shcheglova

Department of Nonlinear Dynamical Systems and Differential Equations, Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia

Abstract: We consider a linear hybrid system with variable coefficients and known mode switching moments under the assumption that matrices at the derivative of the desired vector function are identically degenerate. We obtain the necessary and sufficient conditions for the existence of a piecewise smooth solution (either continuous or not in its definition domain) for the initial problem. We study an equivalent structural form of a nonstationary system of linear differential-algebraic equations with time varying coefficients. We propose a constructive algorithm for obtaining such a form even if the rank of the matrix at the derivative is not constant.

Keywords: hybrid system, differential-algebraic equations, equivalent transformation, solvability, consistent initial data.

Full text: PDF file (243 kB)
References: PDF file   HTML file

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:9, 49–61

Bibliographic databases:

Document Type: Article
UDC: 517.926
Received: 05.11.2008

Citation: A. A. Shcheglova, “The solvability of the initial problem for a degenerate linear hybrid system with variable coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 9, 57–70; Russian Math. (Iz. VUZ), 54:9 (2010), 49–61

Citation in format AMSBIB
\Bibitem{Shc10}
\by A.~A.~Shcheglova
\paper The solvability of the initial problem for a~degenerate linear hybrid system with variable coefficients
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 9
\pages 57--70
\mathnet{http://mi.mathnet.ru/ivm7128}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2789307}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 9
\pages 49--61
\crossref{https://doi.org/10.3103/S1066369X10090057}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649570969}


Linking options:
  • http://mi.mathnet.ru/eng/ivm7128
  • http://mi.mathnet.ru/eng/ivm/y2010/i9/p57

    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. Shcheglova A.A., Matveeva I.I., “On the nonresonance property of linear differential-algebraic systems”, Differ Equ, 48:1 (2012), 26–43  crossref  mathscinet  zmath  isi  elib  elib
    2. P. S. Petrenko, “Detektiruemost lineinykh sistem differentsialno-algebraicheskikh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:3 (2013), 109–116  mathnet
    3. A. A. Scheglova, P. S. Petrenko, “Pravilnye sistemy differentsialno-algebraicheskikh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:4 (2013), 107–127  mathnet
    4. A. A. Shcheglova, S. A. Anishchuk, “An index of linear system of differential-algebraic system with partial derivatives”, Russian Math. (Iz. VUZ), 58:4 (2014), 52–68  mathnet  crossref
    5. P. S. Petrenko, A. A. Shcheglova, “Stabilization of solutions for nonlinear differential-algebraic equations”, Autom. Remote Control, 76:4 (2015), 573–588  mathnet  crossref  isi  elib
    6. A. A. Scheglova, A. D. Kononov, “O robastnoi ustoichivosti sistem differentsialno-algebraicheskikh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 16 (2016), 117–130  mathnet
    7. P. S. Petrenko, “Nablyudaemost v klasse funktsii Chebysheva sistem differentsialno-algebraicheskikh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 20 (2017), 61–74  mathnet  crossref
    8. A. D. Kononov, “O robastnoi ustoichivosti statsionarnykh differentsialno-algebraicheskikh uravnenii so strukturirovannoi neopredelennostyu”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 23 (2018), 20–35  mathnet  crossref
    9. P. S. Petrenko, “Robust controllability of linear differential-algebraic equations with unstructured uncertainty”, J. Appl. Industr. Math., 12:3 (2018), 519–530  mathnet  crossref  crossref  elib  elib
    10. A. A. Shcheglova, “Controllability of differential-algebraic equations in the class of impulse effects”, Siberian Math. J., 59:1 (2018), 166–178  mathnet  crossref  crossref  isi  elib
    11. P. S. Petrenko, “Robastnaya upravlyaemost nestatsionarnykh differentsialno-algebraicheskikh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 79–92  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Number of views:
    This page:276
    Full text:43
    References:28
    First page:6

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