A Multiobservers Approach for a Class of Bidimensional Nonuniformly Observable Systems

We consider the observation problem for a particular class of bidimensional systems with scalar output, which requires the consideration of an embedding in a higher dimension for the usual high-gain observer synthesis. We propose a new approach that does not require any coordinates transformation. This approach is based on the design of a set of estimators running in parallel in the same dimension than the original system. Each estimator uses the knowledge of the first two derivatives of the output, and the further derivatives up to the $m$th one (where $m$ is the observability index over an invariant domain) are used to discriminate at any time among the different estimators. We give two examples showing the applicability of this approach with measurement noise. Biological systems used in batch bioprocess models are of particular motivation for this article.