Observer design with arbitrarily delayed measurements

Francoise Lamnabhi-Lagarrigue

Based on a similar idea than a result from Germani, Manes and Pepe for dealing with delays for finite-dimensional systems, by using a set of chained predictors simultaneously operating, an observer will be here designed for a class of nonlinear parabolic PDEs with delayed point measurements. The novelty lies is that the delay size is arbitrary. To compensate for this arbitrary delay effect, the observer will consist of several chained sub-observers. Each sub-observer compensates a fraction of the global delay. The resulting estimation error system will be shown to be exponentially stable provided that 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.