State observer design for non linear coupled partial differential equations with application to radiative-conductive heat transfer systems
Résumé
This contribution deals with state observer design for a class of non linear coupled PDE that describe radiative-
conductive heat transfer systems. This approach uses first a stable spatial discretization technique that is the Galerkin method to obtain a large scale but finite dimensional system in a suitable form. Thanks to the special structure of the obtained state system, the second main result is to show through the differential mean value theorem (DMVT) that there always exists an observer gain matrix that assures asymptotic convergence. On the other hand, in order to avoid high computational requirements, we show how to construct the observer gain matrix so that the stability condition, written in terms of linear matrix inequality, is satisfied. Extension to $H_\infty$ performance analysis is also proposed. In order to show high accuracy of the proposed technique, a numerical example is provided.