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Lyapunov Functions Obtained from First Order Approximations Read chapter Read first chapter

2017 | OriginalPaper | Chapter

10. Exponential Stability of Semi-linear One-Dimensional Balance Laws

Authors : Georges Bastin, Jean-Michel Coron

Published in: Feedback Stabilization of Controlled Dynamical Systems

Publisher: Springer International Publishing

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Abstract

Raman amplifiers and plug flow chemical reactors are typical examples of engineering systems that are conveniently represented by semi-linear one-dimensional systems of balance laws. The main goal of this chapter is to explain how a quadratic Lyapunov function can be used to prove the exponential stability of the steady state for this class of hyperbolic systems.

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previous chapter Incremental Graphical Asymptotic Stability for Hybrid Dynamical Systems
next chapter Checkable Conditions for Contraction After Small Transients in Time and Amplitude
Footnotes
1
The notation \(M^{\! \mathsf {T}}\) denotes the transpose of the matrix M.
 
Literature
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Metadata
Title
Exponential Stability of Semi-linear One-Dimensional Balance Laws
Authors
Georges Bastin
Jean-Michel Coron
Copyright Year
2017
Book
Feedback Stabilization of Controlled Dynamical Systems

Print ISBN: 978-3-319-51297-6

Electronic ISBN: 978-3-319-51298-3

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-51298-3_10