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
Bibliographical noteFunding 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: firstname.lastname@example.org; email@example.com).
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- Nonlinear control
- robust control