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

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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.
LanguageEnglish
JournalInternational Journal of Control
Early online date28 Jan 2019
DOIs
StatusE-pub ahead of print - 28 Jan 2019

Cite this

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title = "Stability and convergence properties of forced infinite-dimensional discrete-time Lur’e systems",
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.",
author = "Max Gilmore and Christopher Guiver and Hartmut Logemann",
year = "2019",
month = "1",
day = "28",
doi = "10.1080/00207179.2019.1575528",
language = "English",
journal = "International Journal of Control",
issn = "0020-7179",
publisher = "Taylor and Francis",

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T1 - Stability and convergence properties of forced infinite-dimensional discrete-time Lur’e systems

AU - Gilmore, Max

AU - Guiver, Christopher

AU - Logemann, Hartmut

PY - 2019/1/28

Y1 - 2019/1/28

N2 - 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.

AB - 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.

U2 - 10.1080/00207179.2019.1575528

DO - 10.1080/00207179.2019.1575528

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JO - International Journal of Control

T2 - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

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