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

  • Type:

    Article

  • Date:

    24 January 2019

  • Publication Status:

    Published

  • Publisher

    Society for Industrial and Applied Mathematics Publications

  • DOI:

    10.1137/17M1150426

  • Cross Ref:

    10.1137/17M1150426

  • ISSN:

    0363-0129

  • Funders:

    Historic Funder (pre-Worktribe)

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

Authors

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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