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

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

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.

Citation

Guiver, C., Logemann, H., & Opmeer, M. R. (2019). Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties. SIAM Journal on Control and Optimization, 57(1), 334-365. https://doi.org/10.1137/17M1150426

• 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
• DOI: https://doi.org/10.1137/17M1150426
• Keywords: absolute stability, converging-input converging-state property, incremental stability, input-to-state stability, Lur'e systems, infinite-dimensional well-posed linear systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2677259