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2019 | OriginalPaper | Chapter

3. ISS in Spatial L p Norms for Hyperbolic PDEs

Authors : Iasson Karafyllis, Miroslav Krstic

Published in: Input-to-State Stability for PDEs

Publisher: Springer International Publishing

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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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Metadata
Title
ISS in Spatial L p Norms for Hyperbolic PDEs
Authors
Iasson Karafyllis
Miroslav Krstic
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-91011-6_3