Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems

Gilmore, Max E.; Guiver, Chris; Logemann, Hartmut

Abstract

Incremental stability and convergence properties for forced, infinite-dimensional, discrete-time Lur'e systems are addressed. Lur'e systems have a linear and nonlinear component and arise as the feedback interconnection of a linear control system and a static nonlinearity. Discrete-time Lur'e systems arise in, for example, sampled-data control and integro-difference models. We provide conditions, reminiscent of classical absolute stability criteria, which are sufficient for a range of incremental stability properties and input-to-state stability (ISS). Consequences of our results include sufficient conditions for the converging-input converging-state (CICS) property, and convergence to periodic solutions under periodic forcing.

Citation

Gilmore, M. E., Guiver, C., & Logemann, H. (2020). Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems. International Journal of Control, 93(12), 3026-3049. https://doi.org/10.1080/00207179.2019.1575528

• Journal Article Type: Article
• Acceptance Date: Jan 23, 2019
• Online Publication Date: Feb 22, 2019
• Publication Date: 2020
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Jul 23, 2020
• Journal: International Journal of Control
• Print ISSN: 0020-7179
• Electronic ISSN: 1366-5820
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• Volume: 93
• Issue: 12
• Pages: 3026-3049
• DOI: https://doi.org/10.1080/00207179.2019.1575528
• Keywords: Absolute stability, converging-input converging-state p roperty, integral projection models, incremental stability, infinite-dimensional disc rete-time systems, input-to-state stability, Lur’e systems, sampled-data systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2677279