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Avtomatika i Telemekhanika, 2019, Issue 8, Pages 9–28
DOI: https://doi.org/10.1134/S0005231019080038 (Mi at15137) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Nonlinear Systems

Switched systems, Lur’e systems, absolute stability, Aizerman problem

V. A. Kamenetskiy

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (695 kB) Citations (17)
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DOI: https://doi.org/10.1134/S0005231019080038
Abstract: We distinguish a subclass of switched linear systems that we call pairwise connected. We show that the dynamics of such systems can be described by Lur’e systems. For pairwise connected systems, we obtain a sufficient frequency-domain condition for the existence of a quadratic Lyapunov function. The well-known Aizerman problem is reformulated for switched linear systems. We show an example of a system with switchings between three linear third order subsystems for which Aizerman’s problem has a positive solution.
Keywords: switched systems, Lur’e systems, stability, Aizerman problem, Lyapunov functions, matrix inequalities.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.29
This work was supported by the Program of the Presidium of the Russian Academy of Sciences “Modern Problems of Robotics,” project no. I.29.

Received: 11.10.2018
Revised: 26.11.2018
Accepted: 07.02.2019
English version:
Automation and Remote Control, 2019, Volume 80, Issue 8, Pages 1375–1389
DOI: https://doi.org/10.1134/S0005117919080010
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Kamenetskiy, “Switched systems, Lur’e systems, absolute stability, Aizerman problem”, Avtomat. i Telemekh., 2019, no. 8, 9–28; Autom. Remote Control, 80:8 (2019), 1375–1389
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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