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Avtomat. i Telemekh., 2007, Issue 9, Pages 38–55 (Mi at1046)  

This article is cited in 6 scientific papers (total in 6 papers)

Dissipativity of diffusion Itô processes with Markovain switching and problems of robust stabilization

P. V. Pakshin

Arzamas Polytechnical Institute of Nizhni Novgorod State Technical University, Arzamas, Russia

Abstract: Consideration is given to a class of systems described by a finite set of controlled diffusion Itô processes that are control-affine, with jump transitions between them, and are defined by the evolution of a uniform Markovian chain (Markovian switching). Each state of this chain corresponds to a certain system mode. A stochastic version of the notion dissipativity by Willems is introduced, and properties of diffusion processes with Markovian switching are studied. The relationship between passivity and stabilizability in the process of output-feedback control is established. The obtained results are applied to the problem of robust simultaneous stabilization for the set of nonlinear systems with undetermined parameters. As a partial case, a problem of robust simultaneous stabilization for the set of linear systems where final results are obtained in terms of linear matrix inequalities.

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English version:
Automation and Remote Control, 2007, 68:9, 1502–1518

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: Л. Б. Рапопорт

Received: 07.02.2007

Citation: P. V. Pakshin, “Dissipativity of diffusion Itô processes with Markovain switching and problems of robust stabilization”, Avtomat. i Telemekh., 2007, no. 9, 38–55; Autom. Remote Control, 68:9 (2007), 1502–1518

Citation in format AMSBIB
\Bibitem{Pak07}
\by P.~V.~Pakshin
\paper Dissipativity of diffusion It\^o processes with Markovain switching and problems of robust stabilization
\jour Avtomat. i Telemekh.
\yr 2007
\issue 9
\pages 38--55
\mathnet{http://mi.mathnet.ru/at1046}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2360817}
\zmath{https://zbmath.org/?q=an:1145.93044}
\transl
\jour Autom. Remote Control
\yr 2007
\vol 68
\issue 9
\pages 1502--1518
\crossref{https://doi.org/10.1134/S0005117907090056}


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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. Mazurov A.Yu., Pakshin P.V., “Dissipative stochastic differential systems with risk-sensitive storage function and control design problems”, Journal of Computer and Systems Sciences International, 48:5 (2009), 705–717  crossref  mathscinet  zmath  isi  scopus
    2. A. Yu. Mazurov, “Dissipativnost i chuvstvitelnost k riskam v zadachakh upravleniya”, UBS, 29 (2010), 42–67  mathnet
    3. Wu Zh., Cui M., Xie X., Shi P., “Theory of Stochastic Dissipative Systems”, IEEE Trans Automat Control, 56:7 (2011), 1650–1655  crossref  mathscinet  zmath  isi  scopus
    4. Zhang Y., Liu C., Mu X., “Robust finite-time H-infinity control of singular stochastic systems via static output feedback”, Applied Mathematics and Computation, 218:9 (2012), 5629–5640  crossref  mathscinet  zmath  isi  scopus
    5. Zhang Y., Cheng W., Mu X., Guo X., “Observer-Based Finite-Time H-Infinity Control of Singular Markovian Jump Systems”, J. Appl. Math., 2012, 205727  crossref  mathscinet  zmath  isi  scopus
    6. Lin Zh., Liu J., Zhang W., Niu Yu., “a Geometric Approach To H-Infinity Control of Nonlinear Markovian Jump Systems”, Int. J. Control, 87:9 (2014), 1833–1845  crossref  mathscinet  zmath  isi  scopus
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