Abstract

In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman's conjecture (as well as Aizerman's) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of absolute stability, namely, the selection of the class of nonlinear systems whose stability can be studied with linear methods.

Original languageEnglish
Pages (from-to)138-143
Number of pages6
JournalIFAC-PapersOnLine
Volume51
Issue number33
DOIs
Publication statusPublished - 1 Jan 2018

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System stability
Nonlinear systems

Scopus subject areas

  • Control and Systems Engineering

Cite this

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title = "Counterexamples to the Kalman Conjectures⁎",
abstract = "In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman's conjecture (as well as Aizerman's) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of absolute stability, namely, the selection of the class of nonlinear systems whose stability can be studied with linear methods.",
keywords = "Barabanov system, Fitts system, hidden attractor, Kalman conjecture, point-mapping method",
author = "Kuznetsov, {N. V.} and Kuznetsova, {O. A.} and D. Koznov and Mokaev, {R. N.} and B. Andrievsky",
year = "2018",
month = "1",
day = "1",
doi = "10.1016/j.ifacol.2018.12.107",
language = "English",
volume = "51",
pages = "138--143",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "Elsevier",
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T1 - Counterexamples to the Kalman Conjectures⁎

AU - Kuznetsov, N. V.

AU - Kuznetsova, O. A.

AU - Koznov, D.

AU - Mokaev, R. N.

AU - Andrievsky, B.

PY - 2018/1/1

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N2 - In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman's conjecture (as well as Aizerman's) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of absolute stability, namely, the selection of the class of nonlinear systems whose stability can be studied with linear methods.

AB - In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman's conjecture (as well as Aizerman's) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of absolute stability, namely, the selection of the class of nonlinear systems whose stability can be studied with linear methods.

KW - Barabanov system

KW - Fitts system

KW - hidden attractor

KW - Kalman conjecture

KW - point-mapping method

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EP - 143

JO - IFAC-PapersOnLine

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