Name
Title | ||
|---|---|---|
Robustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delays |
Abstract | ||
|---|---|---|
This paper discusses the in-domain feedback stabilization of reaction–diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a C0-semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.automatica.2020.109347 | Automatica |
Keywords | DocType | Volume |
Delayed distributed actuation,Spatially-varying delay,Distributed parameter systems,Predictor feedback,Reaction–diffusion equation | Journal | 123 |
Issue | ISSN | Citations |
1 | 0005-1098 | 1 |
PageRank | References | Authors |
0.35 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lhachemi, H. | 1 | 22 | 8.90 |
| Christophe Prieur | 2 | 1037 | 129.96 |
| Robert Shorten | 3 | 293 | 60.79 |