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Izv. IMI UdGU, 2012, Issue 2(40), Pages 3–164 (Mi iimi230)  

This article is cited in 12 scientific papers (total in 12 papers)

Invariant and statistically weakly invariant sets of control systems

L. I. Rodina

Udmurt State University, 426034, Russia, Izhevsk, ul. Universitetskaya, 1

Abstract: The paper deals with the expansion of the concept of the set invariance with respect to control systems and differential inclusions. Said expansions that statistically invariant and statistically weakly invariant sets are studied. The sufficient conditions for existence of invariant (in the specified sense) sets, which are formulated in terms of the Hausdorff–Bebutov metric, Lyapunov functions and the Clarke derivative, of the given functions are obtained. The work covers both determined systems and the systems with random parameters, for which the concept of statistical invariance with probability one is investigated. The problems about complete controllability of time-varying linear system and about the existence of non-predicting control for linear system with random parameters are considered, too.

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

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UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15
Received: 10.09.2012

Citation: L. I. Rodina, “Invariant and statistically weakly invariant sets of control systems”, Izv. IMI UdGU, 2012, no. 2(40), 3–164

Citation in format AMSBIB
\Bibitem{Rod12}
\by L.~I.~Rodina
\paper Invariant and statistically weakly invariant sets of control systems
\jour Izv. IMI UdGU
\yr 2012
\issue 2(40)
\pages 3--164
\mathnet{http://mi.mathnet.ru/iimi230}


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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. Ya. Yu. Larina, L. I. Rodina, “Statisticheskie kharakteristiki upravlyaemykh sistem, voznikayuschie v razlichnykh modelyakh estestvoznaniya”, Model. i analiz inform. sistem, 20:5 (2013), 62–77  mathnet
    2. L. I. Rodina, A. Kh. Khammadi, “Kharakteristiki mnozhestva dostizhimosti, svyazannye s invariantnostyu upravlyaemoi sistemy na konechnom promezhutke vremeni”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 35–48  mathnet
    3. L. I. Rodina, “O nekotorykh veroyatnostnykh modelyakh dinamiki rosta populyatsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 109–124  mathnet
    4. 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
    5. 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
    6. Ya. Yu. Larina, “Statisticheskie kharakteristiki upravlyaemykh sistem s impulsnym vozdeistviem”, Izv. IMI UdGU, 2015, no. 2(46), 99–105  mathnet  elib
    7. A. Kh. Khammadi, “O svoistvakh kharakteristik mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2015, no. 2(46), 216–227  mathnet  elib
    8. 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
    9. L. I. Rodina, A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2016, no. 1(47), 44–53  mathnet  elib
    10. 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
    11. Ya. Yu. Larina, L. I. Rodina, “Asimptoticheski ustoichivye mnozhestva upravlyaemykh sistem s impulsnym vozdeistviem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:4 (2016), 490–502  mathnet  crossref  mathscinet  elib
    12. L. I. Rodina, “Ob asimptoticheskikh svoistvakh reshenii upravlyaemykh sistem so sluchainymi parametrami”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 189–199  mathnet  crossref  elib
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