Counterexamples to the Kalman Conjectures

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4 Scopus citations


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
Issue number33
StatePublished - 1 Jan 2018

Scopus subject areas

  • Control and Systems Engineering


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

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