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

Guiver, Chris; Logemann, Hartmut; Opmeer, Mark R.


Hartmut Logemann

Mark R. Opmeer


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.

Journal Article Type Article
Acceptance Date Sep 27, 2018
Online Publication Date Jan 24, 2019
Publication Date 2019-03
Deposit Date Jul 23, 2020
Journal SIAM Journal on Control and Optimization
Print ISSN 0363-0129
Electronic ISSN 1095-7138
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 57
Issue 1
Pages 334-365
Keywords absolute stability, converging-input converging-state property, incremental stability, input-to-state stability, Lur'e systems, infinite-dimensional well-posed linear systems
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