Regional observability of distributed systems

The aim of this paper is to develop the concept of regional observability for distributed systems. This original concept is closer to practical considerations since it only requires the observation of the state on a given subregion. We show by means of an example that it is a weaker concept and we describe two approaches. The first one is state space based and can be easily implemented for numerical simulations. Then a second approach leads to the estimation of the state on the considered subregion with a zero residual state.