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Avtomatika i Telemekhanika, 2018, Issue 1, Pages 113–129 (Mi at14972)  
This article is cited in 11 scientific papers (total in 11 papers)

Topical issue

Stochastic stability of some classes of nonlinear 2D systems

P. V. Pakshina, J. P. Emelianovaa, M. A. Emelianova, K. Gałkowskib, E. Rogersc

a Arzamas Polytechnic Institute of R. E. Alekseev Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
b Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland
c Department of Electronics and Computer Science, University of Southampton, Southampton, United Kingdom
Full-text PDF (664 kB) Citations (11)
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Abstract: The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a special case of 2D systems that originate from the modeling of physical processes. Using the vector Lyapunov function method, sufficient conditions for stability in the mean square are obtained in the stochastic setting, where the vast majority of the currently known results are for deterministic dynamics. Based on these results, the property of stochastic exponential passivity in the second moment is used, together with the vector storage function, to develop a new method for output feedback control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate the effectiveness of the new results.
Keywords: 2D systems, discrete repetitive processes, differential repetitive processes, stochastic stability, vector Lyapunov function, passivity, stabilization.
Funding agency Grant number
Russian Foundation for Basic Research 16-08-00916_a
National Science Centre (Narodowe Centrum Nauki) 2015/17/B/ST7/03703
This work was supported in part by the Russian Foundation for Basic Research, project no.16-08-00916_a, and by National Science Centre in Poland, project no. 2015/17/B/ST7/03703.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 20.03.2017
English version:
Automation and Remote Control, 2018, Volume 79, Issue 1, Pages 89–102
DOI: https://doi.org/10.1134/S0005117918010083
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. V. Pakshin, J. P. Emelianova, M. A. Emelianov, K. Gałkowski, E. Rogers, “Stochastic stability of some classes of nonlinear 2D systems”, Avtomat. i Telemekh., 2018, no. 1, 113–129; Autom. Remote Control, 79:1 (2018), 89–102
Citation in format AMSBIB
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\by P.~V.~Pakshin, J.~P.~Emelianova, M.~A.~Emelianov, K.~Ga\l kowski, E.~Rogers
\paper Stochastic stability of some classes of nonlinear 2D systems
\jour Avtomat. i Telemekh.
\yr 2018
\issue 1
\pages 113--129
\mathnet{http://mi.mathnet.ru/at14972}
\elib{https://elibrary.ru/item.asp?id=32317620}
\transl
\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 1
\pages 89--102
\crossref{https://doi.org/10.1134/S0005117918010083}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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