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2019 | OriginalPaper | Chapter

9. Hyperbolic PDE-PDE Loops

Authors : Iasson Karafyllis, Miroslav Krstic

Published in: Input-to-State Stability for PDEs

Publisher: Springer International Publishing

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Abstract

The chapter is devoted to the development of the small-gain methodology for coupled 1-D, hyperbolic, first-order PDEs under the presence of external inputs. Our aim is the derivation of sufficient conditions that guarantee ISS for a given system of coupled hyperbolic PDEs. Globally, Lipschitz nonlinear, non-local terms are allowed to be present both in the PDEs and the boundary conditions. The results are expressed in the spatial sup-norm. The chapter also includes the development of existence/uniqueness results for hyperbolic PDE-PDE loops as well as a detailed comparison with existing results in the literature.

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Metadata
Title
Hyperbolic PDE-PDE Loops
Authors
Iasson Karafyllis
Miroslav Krstic
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-91011-6_9