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Avtomat. i Telemekh., 2006, Issue 11, Pages 122–158 (Mi at1300)  

This article is cited in 9 scientific papers (total in 9 papers)

Stochastic problems of absolute stability

P. V. Pakshina, V. A. Ugrinovskiib

a Arzamas Polytechnical Institute of the Nizhni Novgorod State Technical University, Arzamas, Russia
b University of New South Wales, Canberra, Australia

Abstract: The publications concerned with the development of the theory of absolute stability of stochastic systems were reviewed. The criteria for absolute stochastic stability based on the V. A. Yakubovich frequency theorem and algebraic approaches which do not use the frequency theorem were presented. A stochastic analog of the frequency theorem was formulated, and its features were discussed. A relation between the problems of absolute stochastic stability and optimal stochastic control was established. The results on some problems of stochastic stabilization based on the frequency theorem were considered. Some criteria for stochastic stability of the pulse systems established on basis of the frequency theorem were presented. The problems of passivity and dissipativity of the nonlinear stochastic systems were discussed. The state-of-the-art of the theory was briefly characterized in conclusion.

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English version:
Automation and Remote Control, 2006, 67:11, 1811–1846

Bibliographic databases:

PACS: 02.30.Yy, 01.30.Rr
Presented by the member of Editorial Board: Б. Т. Поляк

Received: 06.02.2006

Citation: P. V. Pakshin, V. A. Ugrinovskii, “Stochastic problems of absolute stability”, Avtomat. i Telemekh., 2006, no. 11, 122–158; Autom. Remote Control, 67:11 (2006), 1811–1846

Citation in format AMSBIB
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\paper Stochastic problems of absolute stability
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\pages 122--158
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\transl
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\yr 2006
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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. M. R. Liberzon, “Essays on the absolute stability theory”, Autom. Remote Control, 67:10 (2006), 1610–1644  mathnet  crossref  mathscinet  zmath  elib  elib
    2. P. V. Pakshin, “Dissipativity of diffusion Itô processes with Markovain switching and problems of robust stabilization”, Autom. Remote Control, 68:9 (2007), 1502–1518  mathnet  crossref  mathscinet  zmath
    3. P. V. Pakshin, “Exponential dissipativeness of the random-structure diffusion processes and problems of robust stabilization”, Autom. Remote Control, 68:10 (2007), 1852–1870  mathnet  crossref  mathscinet  zmath
    4. L. B. Ryashko, I. A. Bashkirtseva, “On control of stochastic sensitivity”, Autom. Remote Control, 69:7 (2008), 1171–1180  mathnet  crossref  mathscinet  zmath  isi
    5. M. E. Shaikin, “Representation of the bilinear system output by multiple stochastic integrals”, Autom. Remote Control, 71:6 (2010), 1048–1063  mathnet  crossref  mathscinet  zmath  isi
    6. Dragan V., Morozan T., “A class of discrete time generalized Riccati equations”, J Differ Equations Appl, 16:4 (2010), 291–320  crossref  mathscinet  zmath  isi  elib  scopus
    7. Zhang Q., Zhang W., “Properties of storage functions and applications to nonlinear stochastic H (a) control”, Journal of Systems Science & Complexity, 24:5 (2011), 850–861  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Canto B., Canto R., Kostova S., “Stabilization of Positive Linear Discrete-Time Systems By Using a Brauer'S Theorem”, Sci. World J., 2014, 856356  crossref  isi  scopus
    9. Zhang Y. Zhao Yu. Xu T. Liu X., “Pth Moment Absolute Exponential Stability of Stochastic Control System With Markovian Switching”, J. Ind. Manag. Optim., 12:2 (2016), 471–486  crossref  mathscinet  zmath  isi
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