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.
Main Authors
Format
Conferences
Conference paper
Published
2018
Series
Subjects
Publication in research information system
Publisher
IFAC; Elsevier Ltd.
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201901021008Use this for linking
Review status
Peer reviewed
ISSN
2405-8963
DOI
https://doi.org/10.1016/j.ifacol.2018.12.107
Conference
IFAC Conference on Analysis and Control of Chaotic Systems
Language
English
Published in
IFAC-PapersOnLine
Is part of publication
CHAOS 2018 : 5th IFAC Conference on Analysis and Control of Chaotic Systems, Eindhoven, The Netherlands, 30 October – 1 November 2018
Citation
- Kuznetsov, N., Kuznetsova, O. A., Koznov, D. V., Mokaev, R. N., & Andrievsky, B. (2018). Counterexamples to the Kalman Conjectures. In E. Lefeber (Ed.), CHAOS 2018 : 5th IFAC Conference on Analysis and Control of Chaotic Systems, Eindhoven, The Netherlands, 30 October – 1 November 2018 (pp. 138-143). IFAC; Elsevier Ltd.. IFAC-PapersOnLine, 51. https://doi.org/10.1016/j.ifacol.2018.12.107
License
Copyright© 2018, IFAC.