# Sampled-Data Boundary Feedback Control of 1-D Parabolic PDEs

arXiv: https://arxiv.org/abs/1701.01955 · HTML: https://mlsanity.com/paper/1701.01955/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)

## Abstract (arXiv)

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear parabolic systems on bounded domains. It is shown that the continuous-time boundary feedback applied in a sample-and-hold fashion guarantees closed-loop exponential stability, provided that the sampling period is sufficiently small. Two different continuous-time feedback designs are considered: the reduced model design and the backstepping design. The obtained results provide stability estimates for weighted 2-norms of the state and robustness with respect to perturbations of the sampling schedule is guaranteed.