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Aizerman Conjectures for a class of multivariate positive systems

Drummond, Ross; Guiver, Chris; Turner, Matthew


Ross Drummond

Matthew Turner


The Aizerman Conjecture predicts stability for a class of nonlinear control systems on the basis of linear system stability analysis. The conjecture is known to be false in general. Here, a number of Aizerman conjectures are shown to be true for a class of internally positive multivariate systems, under a natural generalisation of the classical sector condition and, moreover, guarantee positivity in closed loop. These results are stronger and/or more general than existing results. The paper relates the obtained results to other, diverse, results in the literature.

Journal Article Type Article
Acceptance Date Oct 9, 2022
Online Publication Date Oct 27, 2022
Publication Date 2023-08
Deposit Date Oct 19, 2022
Publicly Available Date Oct 27, 2022
Journal IEEE Transactions on Automatic Control
Print ISSN 0018-9286
Electronic ISSN 1558-2523
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 68
Issue 8
Pages 5073 - 5080
Keywords Linear systems, Standards, Stability criteria, Nonlinear systems, Linear matrix inequalities, Asymptotic stability, Transfer functions
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Aizerman Conjectures For A Class Of Multivariate Positive Systems (accepted version) (389 Kb)

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