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Article Dans Une Revue Automatica Année : 2021

Robustness of constant-delay predictor feedback for in-domain stabilization of reaction-diffusion PDEs with time- and spatially-varying input delays

Résumé

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 $C_0$-semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent.
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Dates et versions

hal-02999899 , version 1 (11-11-2020)

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Hugo Lhachemi, Christophe Prieur, Robert Shorten. Robustness of constant-delay predictor feedback for in-domain stabilization of reaction-diffusion PDEs with time- and spatially-varying input delays. Automatica, 2021, 123, pp.109347. ⟨10.1016/j.automatica.2020.109347⟩. ⟨hal-02999899⟩
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