Avtomatika i Telemekhanika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Avtomat. i Telemekh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Avtomatika i Telemekhanika, 2022, Issue 9, Pages 55–80
DOI: https://doi.org/10.31857/S0005231022090033 (Mi at16037) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Nonlinear Systems

Discrete-time pairwise connected switched systems and Lur’e systems. Tsypkin’s criterion for systems with two nonlinearities

V. A. Kamenetskiy

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
Full-text PDF (300 kB) First page Citations (8)
References:
PDF
HTML
DOI: https://doi.org/10.31857/S0005231022090033
Abstract: We study the stability of discrete-time switched systems for any laws of switching between linear subsystems. Pairwise connected systems are distinguished among such systems. A sufficient frequency-domain stability condition has been obtained for them. Two sufficient conditions and two criteria for the existence of a Lyapunov quadratic function are obtained for switched systems whose stability is equivalent to the absolute stability of Lur'e systems with two nonlinearities. These conditions amount to checking the solvability of special matrix inequalities whose dimensions are considerably lower than the dimension of the original system of matrix inequalities that defines the necessary and sufficient conditions. The resulting conditions are compared with the conditions of the Tsypkin criterion and with the necessary and sufficient conditions using the examples of systems of the third and sixth orders.
Keywords: discrete-time switched system, Lur'e system, stability, Lyapunov function, matrix inequality.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the Program of Fundamental Scientific Research in Priority Areas determined by the Presidium of the Russian Academy of Sciences, no. 7 “New developments in promising areas of energy, mechanics, and robotics.”
Presented by the member of Editorial Board: P. V. Pakshin

Received: 21.02.2022
Revised: 28.04.2022
Accepted: 10.06.2022
English version:
Automation and Remote Control, 2022, Volume 83, Issue 9, Pages 1371–1392
DOI: https://doi.org/10.1134/S000511792209003X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Kamenetskiy, “Discrete-time pairwise connected switched systems and Lur’e systems. Tsypkin’s criterion for systems with two nonlinearities”, Avtomat. i Telemekh., 2022, no. 9, 55–80; Autom. Remote Control, 83:9 (2022), 1371–1392
Citation in format AMSBIB
\Bibitem{Kam22}
\by V.~A.~Kamenetskiy
\paper Discrete-time pairwise connected switched systems and Lur’e systems. Tsypkin’s criterion for systems with two nonlinearities
\jour Avtomat. i Telemekh.
\yr 2022
\issue 9
\pages 55--80
\mathnet{http://mi.mathnet.ru/at16037}
\crossref{https://doi.org/10.31857/S0005231022090033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4504831}
\edn{https://elibrary.ru/AILKNJ}
\transl
\jour Autom. Remote Control
\yr 2022
\vol 83
\issue 9
\pages 1371--1392
\crossref{https://doi.org/10.1134/S000511792209003X}
Linking options:
  • https://www.mathnet.ru/eng/at16037
  • https://www.mathnet.ru/eng/at/y2022/i9/p55
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Avtomatika i Telemekhanika
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024