Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties

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Abstract

We consider forced Lur'e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial differential equations are known to belong to this class of infinite-dimensional systems. We investigate input-to-state stability (ISS) and incremental ISS properties: our results are reminiscent of well-known absolute stability criteria such as the complex Aizerman conjecture and the circle criterion. The incremental ISS results are used to derive certain convergence properties, namely the converging-input converging-state (CICS) property and asymptotic periodicity of the state and output under periodic forcing. In particular, we provide sufficient conditions for ISS and incremental ISS. The theory is illustrated with examples.


LanguageEnglish
Pages334-365
Number of pages32
JournalSIAM Journal on Control and Optimization
Volume57
Issue number1
Early online date24 Jan 2019
DOIs
StatusPublished - 2019

Cite this

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title = "Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties",
abstract = "We consider forced Lur'e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial differential equations are known to belong to this class of infinite-dimensional systems. We investigate input-to-state stability (ISS) and incremental ISS properties: our results are reminiscent of well-known absolute stability criteria such as the complex Aizerman conjecture and the circle criterion. The incremental ISS results are used to derive certain convergence properties, namely the converging-input converging-state (CICS) property and asymptotic periodicity of the state and output under periodic forcing. In particular, we provide sufficient conditions for ISS and incremental ISS. The theory is illustrated with examples.",
author = "Christopher Guiver and Hartmut Logemann and Mark Opmeer",
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T1 - Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties

AU - Guiver, Christopher

AU - Logemann, Hartmut

AU - Opmeer, Mark

PY - 2019

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N2 - We consider forced Lur'e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial differential equations are known to belong to this class of infinite-dimensional systems. We investigate input-to-state stability (ISS) and incremental ISS properties: our results are reminiscent of well-known absolute stability criteria such as the complex Aizerman conjecture and the circle criterion. The incremental ISS results are used to derive certain convergence properties, namely the converging-input converging-state (CICS) property and asymptotic periodicity of the state and output under periodic forcing. In particular, we provide sufficient conditions for ISS and incremental ISS. The theory is illustrated with examples.

AB - We consider forced Lur'e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial differential equations are known to belong to this class of infinite-dimensional systems. We investigate input-to-state stability (ISS) and incremental ISS properties: our results are reminiscent of well-known absolute stability criteria such as the complex Aizerman conjecture and the circle criterion. The incremental ISS results are used to derive certain convergence properties, namely the converging-input converging-state (CICS) property and asymptotic periodicity of the state and output under periodic forcing. In particular, we provide sufficient conditions for ISS and incremental ISS. The theory is illustrated with examples.

U2 - 10.1137/17M1150426

DO - 10.1137/17M1150426

M3 - Article

VL - 57

SP - 334

EP - 365

JO - SIAM Journal on Control and Optimization

T2 - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 1

ER -