The article revisits Aizerman and Kalman conjectures for absolute stability through the lens of a novel graphical interpretation. Even though these conjectures are false in the general case, such a graphical interpretation suggests natural ways to introduce additional conditions in order to obtain valid absolute stability criteria. As an illustration, the article proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion.
Revisiting Kalman and Aizerman conjectures / Naderi, Taher; Materassi, Donatello; Innocenti, Giacomo; Genesio, Roberto; Salapaka, Murti V.. - ELETTRONICO. - IEEE Xplore 23 January 2018:(2017), pp. 523-528. (Intervento presentato al convegno 56th IEEE Annual Conference on Decision and Control, CDC 2017 tenutosi a Melbourne Convention and Exhibition Centre (MCEC), (AUS) nel 2017) [10.1109/CDC.2017.8263717].
Revisiting Kalman and Aizerman conjectures
Materassi, Donatello;Innocenti, Giacomo
;Genesio, Roberto;
2017
Abstract
The article revisits Aizerman and Kalman conjectures for absolute stability through the lens of a novel graphical interpretation. Even though these conjectures are false in the general case, such a graphical interpretation suggests natural ways to introduce additional conditions in order to obtain valid absolute stability criteria. As an illustration, the article proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion.
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