Observer design for a class of parabolic systems with large delays and sampled measurements

Tarek Ahmed-Ali (1) , Emilia Fridman (2) , Fouad Giri (3) , Mohamed Kahelras (4) , Françoise Lamnabhi-Lagarrigue (4) , Laurent Burlion (5)

1 ENSICAEN - École Nationale Supérieure d'Ingénieurs de Caen
2 Department of Electrical Engineering
3 Equipe Automatique - Laboratoire GREYC - UMR6072
4 L2S - Laboratoire des signaux et systèmes
5 Rutgers - Rutgers University System

In this paper, we design a novel observer for a class of semilinear heat 1D equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of sub-observers. Each sub-observer handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of sub-observers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of LMIs.

Domains: Automatic

Tarek Ahmed-Ali, Emilia Fridman, Fouad Giri, Mohamed Kahelras, Françoise Lamnabhi-Lagarrigue, et al.. Observer design for a class of parabolic systems with large delays and sampled measurements. IEEE Transactions on Automatic Control, 2019, pp.1-1. ⟨10.1109/TAC.2019.2941434⟩. ⟨hal-02409383⟩