Finite-dimensionnal sampled-data observer for a class of ODE-PDE systems

The present contribution deals with the design of sampled-data observers for a cascade ODE (Ordinary Differential Equation) -PDE (Partial Differential Equation) Systems. The PDE part is constituted by a Heat equation. We extend some existing results to sampled-data case by using the inter-sample output predictor approach. The main feature of the present work is the fact that our observer is a finite dimensional one and provide us exponential convergence of observation error for both finite and infinite-dimensional parts of the cascade ODE-PDE.