Notes on the nested observers for hybrid systems

In this paper a hybrid observer for hybrid systems is presented. The continuous time and the discrete event dynamics are determined in such a way that the observation problem is solved. The observer is built using a nested structure, in which the nesting is due to a refinement of those states corresponding to undecided cases. The continuous dynamics implement an estimator which extracts extra information from the continuous dynamics associated to the discrete event state. These information are based on the convergence ratio of the output estimate to the system output. The resulting continuous dynamics are not simply those of a Luenberger´s observer.