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ISS in Spatial Lp Norms for Hyperbolic PDEs

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Input-to-State Stability for PDEs

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Abstract

The chapter deals with the derivation of ISS estimates expressed in spatial \( L^{p} \) norms for 1-D, first-order, hyperbolic PDEs with a constant transport velocity. Two different methodologies for deriving ISS estimates are provided. The first methodology is the use of ISS-Lyapunov Functionals (ISS-LFs). The second methodology utilizes the transformation to a system of Integral Delay Equations (IDEs). The latter methodology provides ISS estimates expressed only in the sup-norm of the state and the derivation of the ISS estimate is performed by using a Lyapunov-like function (not a functional). Finally, the differences between the two methodologies are explained in detail.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Iasson Karafyllis

  2. Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA

    Miroslav Krstic

Authors
  1. Iasson Karafyllis
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  2. Miroslav Krstic
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Correspondence to Iasson Karafyllis .

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Karafyllis, I., Krstic, M. (2019). ISS in Spatial Lp Norms for Hyperbolic PDEs. In: Input-to-State Stability for PDEs. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-91011-6_3

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