On the uniform input-to-state stability of reaction-diffusion systems

Titelangaben

Dashkovskiy, Sergey ; Mironchenko, Andrii:
On the uniform input-to-state stability of reaction-diffusion systems.
In: 49th IEEE Conference on Decision and Control (CDC) : Proceedings. - Piscataway, NJ, USA : IEEE , 2010 . - S. 6547-6552
ISBN 978-1-4244-7745-6
DOI: https://doi.org/10.1109/CDC.2010.5717779

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Abstract

In the present paper we consider uniform input-to-state stability of reaction-diffusion equations and compare it with its finite dimensional counterpart without diffusion as a parameterized set of decoupled equations. The reaction-diffusion partial differential equation can be seen as their interconnection via diffusion. We prove, that for linear reaction-diffusion systems and certain classes of nonlinear equations the UISS property for corresponding systems without diffusion implies, that the UISS property holds also for the system with diffusion.