Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation

Taher Naderi; Donatello Materassi; Giacomo Innocenti; Roberto Genesio

doi:10.1109/TAC.2018.2849597

Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation

Taher Naderi, Donatello Materassi, Giacomo Innocenti, Roberto Genesio

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

6 Scopus citations

Abstract

The paper revisits Aizerman and Kalman conjectures for absolute stability through the lens of a novel graphical interpretation. Even though these conjectures have been proven false, such a graphical interpretation suggests natural ways to introduce additional conditions in order to obtain new valid absolute stability criteria. As an illustration, the paper proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion

Original language	English (US)
Article number	8392461
Pages (from-to)	670-682
Number of pages	13
Journal	IEEE Transactions on Automatic Control
Volume	64
Issue number	2
DOIs	https://doi.org/10.1109/TAC.2018.2849597
State	Published - 2019
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received April 12, 2017; revised November 16, 2017; accepted March 22, 2018. Date of publication June 21, 2018; date of current version January 28, 2019. This work was partially supported by ARPA-E NODES. Recommended by Associate Editor C. M. Kellet. (Corresponding author: Taher Naderi.) T. Naderi and D. Materassi are with the Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN 37996, USA (email: tnaderi@utk.edu; dmateras@utk.edu).

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

Nonlinear control
optimization
robust control

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10.1109/TAC.2018.2849597

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abstract = "The paper revisits Aizerman and Kalman conjectures for absolute stability through the lens of a novel graphical interpretation. Even though these conjectures have been proven false, such a graphical interpretation suggests natural ways to introduce additional conditions in order to obtain new valid absolute stability criteria. As an illustration, the paper proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion",

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Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation

Abstract

Bibliographical note

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