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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 11, Pages 20–32 (Mi ivm8843)  

This article is cited in 8 scientific papers (total in 8 papers)

Estimation of statistical characteristics of attainability sets of controllable systems

L. I. Rodina

Chair of Mathematical Analysis, Udmurt State University, 1 Universitetskaya str., Izhevsk, 426034 Russia

Abstract: We study an expansion of the notion of invariance for sets with respect to controllable systems and differential inclusions. Namely, we study statistically invariant sets and statistical characteristics of attainability sets of controllable systems. We obtain a lower bound for the lower relative frequency of the absorption of the attainability set of a system by a given set and establish new sufficient conditions of the statistical invariance of the set with respect to the controllable system. We give examples of the calculation of statistical characteristics for the linear Cauchy problem and a linear controllable system with almost periodic coefficients.

Keywords: controllable systems, dynamical systems, differential inclusions, statistically invariant sets.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:11, 17–27

UDC: 517.977
Received: 23.07.2012

Citation: L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 11, 20–32; Russian Math. (Iz. VUZ), 57:11 (2013), 17–27

Citation in format AMSBIB
\Bibitem{Rod13}
\by L.~I.~Rodina
\paper Estimation of statistical characteristics of attainability sets of controllable systems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 11
\pages 20--32
\mathnet{http://mi.mathnet.ru/ivm8843}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 11
\pages 17--27
\crossref{https://doi.org/10.3103/S1066369X13110029}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888323060}


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    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. A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemykh sistem so sluchainymi koeffitsientami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 100–110  mathnet
    2. L. I. Rodina, A. Kh. Khammadi, “Statistical characteristics of attainability set of controllable systems with random coefficients”, Russian Math. (Iz. VUZ), 58:11 (2014), 43–53  mathnet  crossref
    3. Ya. Yu. Larina, “Funktsii Lyapunova i teoremy sravneniya dlya upravlyaemykh sistem s impulsnym vozdeistviem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 51–59  mathnet  elib
    4. Ya. Yu. Larina, “Statisticheskie kharakteristiki upravlyaemykh sistem s impulsnym vozdeistviem”, Izv. IMI UdGU, 2015, no. 2(46), 99–105  mathnet  elib
    5. A. Kh. Khammadi, “O svoistvakh kharakteristik mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2015, no. 2(46), 216–227  mathnet  elib
    6. Ya. Yu. Larina, “O slaboi asimptoticheskoi ustoichivosti upravlyaemykh sistem s impulsnym vozdeistviem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:1 (2016), 68–78  mathnet  crossref  mathscinet  elib
    7. L. I. Rodina, A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2016, no. 1(47), 44–53  mathnet  elib
    8. Ya. Yu. Larina, L. I. Rodina, “Statistical characteristics of continuous functions and statistically weakly invariant sets of controllable system”, Russian Math. (Iz. VUZ), 61:2 (2017), 28–35  mathnet  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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