Feedback Stabilization of a 1-D Linear Reaction–Diffusion Equation With Delay Boundary Control

@article{Prieur2019FeedbackSO,
  title={Feedback Stabilization of a 1-D Linear Reaction–Diffusion Equation With Delay Boundary Control},
  author={C. Prieur and E. Tr{\'e}lat},
  journal={IEEE Transactions on Automatic Control},
  year={2019},
  volume={64},
  pages={1415-1425}
}
  • C. Prieur, E. Trélat
  • Published 2019
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
The goal of this paper is to design a stabilizing feedback boundary control for a reaction–diffusion partial differential equation (PDE), where the boundary control is subject to a constant delay while the equation may be unstable without any control. For this system, which is equivalent to a parabolic equation coupled with a transport equation, a prediction-based control is explicitly computed by splitting the infinite-dimensional system into two parts: a finite-dimensional unstable part and a… Expand
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