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

Christopher Guiver, Hartmut Logemann, Mark Opmeer

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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.

Original languageEnglish
Pages (from-to)334-365
Number of pages32
JournalSIAM Journal on Control and Optimization
Issue number1
Early online date24 Jan 2019
Publication statusPublished - 31 Dec 2019


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