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

Hugo Lhachemi (1) , Robert Shorten (2, 1)

1 UCD - University College Dublin [Dublin]
2 Imperial College London

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.

Domaines: Optimisation et contrôle [math.OC]

Hugo Lhachemi, Robert Shorten. Boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and state-delay. Automatica, 2020, 116, pp.108931. ⟨10.1016/j.automatica.2020.108931⟩. ⟨hal-03133676⟩