Embedding for exponential observers of nonlinear systems

For nonlinear systems in Rⁿ which admit an observability index m strictly larger than n, we show that under the existence of an injective immersion onto a manifold of R^m , one can build an exponential observer. The main point concerns the determination of a Lipschitz extension to R^m of the dynamics, which is defined only on a manifold of dimension n. We propose some constructive tools and illustrate their utility on a simple biological model