Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Gilmore, Max E.; Guiver, Chris; Logemann, Hartmut
• Is Part Of: International journal of control. Volume 93:Issue 12(2020)
• Page Start: 3026
• Page End: 3049
• Publication Date: 2020-12-01
• Subjects: Absolute stability -- converging-input converging-state property -- integral projection models -- incremental stability -- infinite-dimensional discrete-time systems -- input-to-state stability -- Lur'e systems -- sampled-data systems; 93C05 -- 93C10 -- 93C35 -- 93C55 -- 93C57 -- 93D05 -- 93D15 -- 93D20; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2019.1575528
• Languages: English
• ISSNs: 0020-7179

Abstract

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.