This work is about state estimation in the bounded error context for non linear continuous time systems. The main idea is to seek to estimate not an optimal value for the unknown state vector but the set of feasible values, thus to characterize simultaneously the value of the vector and its uncertainty. Our contribution resides in the use of comparison theorems for differential inequalities and the analysis of the monotonicity of the dynamical systems with respect to the uncertain variables. The uncertain dynamical system is then bracketed between two hybrid dynamical systems. We show how to obtain this systems and to use them for state estimation with a prediction-correction type observer. An example is given with bioreactors.
