Aizerman Conjectures for a class of multivariate positive systems

Drummond, Ross; Guiver, Chris; Turner, Matthew

Abstract

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
• DOI: https://doi.org/10.1109/TAC.2022.3217740
• Keywords: Linear systems, Standards, Stability criteria, Nonlinear systems, Linear matrix inequalities, Asymptotic stability, Transfer functions
• Public URL: http://researchrepository.napier.ac.uk/Output/2936363
• Publisher URL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9