The article 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 article proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion.
Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation / Naderi, Taher; Materassi, Donatello; Innocenti, Giacomo; Genesio, Roberto. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - ELETTRONICO. - 64:(2018), pp. 670-682. [10.1109/TAC.2018.2849597]
Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation
Materassi, Donatello;Innocenti, Giacomo
;Genesio, Roberto
2018
Abstract
The article 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 article proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion.
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