Boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and state-delay

Hugo Lhachemi; Robert Shorten

doi:10.1016/j.automatica.2020.108931

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arXiv · 1911.10761

Boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and state-delay

Hugo Lhachemi·Robert Shorten

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Abstract

This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we show that the closed-loop system is exponentially input-to-state stable with fading memory.

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BibTeX RIS

Hugo Lhachemi, Robert Shorten. 2020-03-16. Boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and state-delay. https://doi.org/10.1016/j.automatica.2020.108931

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