The converging-input converging-state property for Lur’e systems

Bill, Adam; Guiver, Chris; Logemann, Hartmut; Townley, Stuart

Abstract

Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur{\textquoteright}e systems, we derive necessary and sufficient conditions for a class of Lur{\textquoteright}e systems to have the converging-input converging-state (CICS) property. In particular, we provide sufficient conditions for CICS which are reminiscent of the complex Aizerman conjecture and the circle criterion and connections are also made with small gain ISS theorems. The penultimate section of the paper is devoted to non-negative Lur{\textquoteright}e systems which arise naturally in, for example, ecological and biochemical applications: the main result in this context is a sufficient criterion for a so-called “quasi CICS” property for Lur{\textquoteright}e systems which, when uncontrolled, admit two equilibria. The theory is illustrated with numerous examples.

Citation

Bill, A., Guiver, C., Logemann, H., & Townley, S. (2017). The converging-input converging-state property for Lur’e systems. Mathematics of Control, Signals, and Systems, 29, Article 4 (2017). https://doi.org/10.1007/s00498-016-0184-3

• Journal Article Type: Article
• Acceptance Date: Dec 19, 2016
• Online Publication Date: Jan 20, 2017
• Publication Date: 2017
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Jul 24, 2020
• Journal: Mathematics of Control, Signals, and Systems
• Print ISSN: 0932-4194
• Electronic ISSN: 1435-568X
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Article Number: 4 (2017)
• DOI: https://doi.org/10.1007/s00498-016-0184-3
• Keywords: Absolute stability, Circle criterion, Converging-input converging-state property, Input-to-state stability, Lur’e systems, Non-negative systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2677309