On counter-examples to Aizerman and Kalman conjectures

I. M. Boiko; N. V. Kuznetsov; R. N. Mokaev; T. N. Mokaev; M. V. Yuldashev; R. V. Yuldashev

doi:10.1080/00207179.2020.1830304

On counter-examples to Aizerman and Kalman conjectures

I. M. Boiko
, N. V. Kuznetsov
, R. N. Mokaev
, T. N. Mokaev
, M. V. Yuldashev
, R. V. Yuldashev

Electrical Engineering

Saint-Petersburg State University

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Counter-examples to Aizerman's and Kalman's conjectures are considered. Investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done. The simultaneous existence of both: a limit cycle and asymptotic or finite-time convergence is proved through the LPRS method and the Lyapunov method, respectively. Conclusions regarding the complex behaviour of these nonlinear dynamic systems are given.

Original language	British English
Pages (from-to)	906-913
Number of pages	8
Journal	International Journal of Control
Volume	95
Issue number	4
DOIs	https://doi.org/10.1080/00207179.2020.1830304
State	Published - 2022

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title = "On counter-examples to Aizerman and Kalman conjectures",

abstract = "Counter-examples to Aizerman's and Kalman's conjectures are considered. Investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done. The simultaneous existence of both: a limit cycle and asymptotic or finite-time convergence is proved through the LPRS method and the Lyapunov method, respectively. Conclusions regarding the complex behaviour of these nonlinear dynamic systems are given.",

author = "Boiko, \{I. M.\} and Kuznetsov, \{N. V.\} and Mokaev, \{R. N.\} and Mokaev, \{T. N.\} and Yuldashev, \{M. V.\} and Yuldashev, \{R. V.\}",

note = "Funding Information: The authors gratefully acknowledge the support of the Russian Science Foundation [grant number 19-41-02002], and Khalifa University of Science, Technology and Research, UAE, project [grant number CIRA-2018-104]. The authors gratefully acknowledge the support of the Russian Science Foundation, grant 19-41-02002, and Khalifa University, UAE, project CIRA-2018-104. Funding Information: The authors gratefully acknowledge the support of the Russian Science Foundation, grant 19-41-02002, and Khalifa University, UAE, project CIRA-2018-104. Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor \& Francis Group.",

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doi = "10.1080/00207179.2020.1830304",

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AU - Boiko, I. M.

AU - Kuznetsov, N. V.

AU - Mokaev, R. N.

AU - Mokaev, T. N.

AU - Yuldashev, M. V.

AU - Yuldashev, R. V.

N1 - Funding Information: The authors gratefully acknowledge the support of the Russian Science Foundation [grant number 19-41-02002], and Khalifa University of Science, Technology and Research, UAE, project [grant number CIRA-2018-104]. The authors gratefully acknowledge the support of the Russian Science Foundation, grant 19-41-02002, and Khalifa University, UAE, project CIRA-2018-104. Funding Information: The authors gratefully acknowledge the support of the Russian Science Foundation, grant 19-41-02002, and Khalifa University, UAE, project CIRA-2018-104. Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - Counter-examples to Aizerman's and Kalman's conjectures are considered. Investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done. The simultaneous existence of both: a limit cycle and asymptotic or finite-time convergence is proved through the LPRS method and the Lyapunov method, respectively. Conclusions regarding the complex behaviour of these nonlinear dynamic systems are given.

AB - Counter-examples to Aizerman's and Kalman's conjectures are considered. Investigation of the behaviour in the vicinity of the origin and at a distance from the origin is done. The simultaneous existence of both: a limit cycle and asymptotic or finite-time convergence is proved through the LPRS method and the Lyapunov method, respectively. Conclusions regarding the complex behaviour of these nonlinear dynamic systems are given.

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VL - 95

SP - 906

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JO - International Journal of Control

JF - International Journal of Control

IS - 4

ER -

On counter-examples to Aizerman and Kalman conjectures

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