Observer Design for a Class of Parabolic Systems with Large Delays and Sampled Measurements

In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) 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 subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs).