Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation

Revisiting Kalman and Aizerman Conjectures via a Graphical Interpretation

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...

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Veröffentlicht in:IEEE transactions on automatic control 2019-02, Vol.64 (2), p.670-682
Hauptverfasser: Naderi, Taher, Materassi, Donatello, Innocenti, Giacomo, Genesio, Roberto
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic stability
Circle criterion
Kalman filters
Linear systems
Nonlinear control
Numerical stability
optimization
robust control
Stability criteria
Transfer functions
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Zusammenfassung: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
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2849597