Counterexamples to the Kalman Conjectures

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4 Scopus citations

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
StatePublished - 1 Jan 2018

Scopus subject areas

  • Control and Systems Engineering

Keywords

  • Barabanov system
  • Fitts system
  • hidden attractor
  • Kalman conjecture
  • point-mapping method

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