Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

Max E. Gilmore; Chris Guiver; Hartmut Logemann

doi:10.1016/j.jde.2021.08.009

Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

Max E. Gilmore, Chris Guiver, Hartmut Logemann

Edinburgh Napier University

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

Abstract

We prove (integral) input-to-state stability results for a class of forced Lur'e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur'e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur'e equations generated by Stepanov almost periodic inputs.

Original language	English
Pages (from-to)	692-733
Number of pages	42
Journal	Journal of Differential Equations
Volume	300
Early online date	19 Aug 2021
DOIs	https://doi.org/10.1016/j.jde.2021.08.009
Publication status	Published - 5 Nov 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

Absolute stability
Almost periodic functions
Circle criterion
Differential inclusions
Incremental (integral) input-to-state stability
Lur'e systems

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2021.08.009

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abstract = "We prove (integral) input-to-state stability results for a class of forced Lur'e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur'e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur'e equations generated by Stepanov almost periodic inputs.",

keywords = "Absolute stability, Almost periodic functions, Circle criterion, Differential inclusions, Incremental (integral) input-to-state stability, Lur'e systems",

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AU - Gilmore, Max E.

AU - Guiver, Chris

AU - Logemann, Hartmut

PY - 2021/11/5

Y1 - 2021/11/5

N2 - We prove (integral) input-to-state stability results for a class of forced Lur'e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur'e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur'e equations generated by Stepanov almost periodic inputs.

AB - We prove (integral) input-to-state stability results for a class of forced Lur'e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur'e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur'e equations generated by Stepanov almost periodic inputs.

KW - Absolute stability

KW - Almost periodic functions

KW - Circle criterion

KW - Differential inclusions

KW - Incremental (integral) input-to-state stability

KW - Lur'e systems

UR - http://www.scopus.com/inward/record.url?scp=85113185551&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2021.08.009

DO - 10.1016/j.jde.2021.08.009

M3 - Article

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SN - 0022-0396

VL - 300

SP - 692

EP - 733

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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