Ellipsoidal Calculus, Singular Perturbations and the State Estimation Problems for Uncertain Systems

One of the basic elements of dynamic modelling of complex systems is the linkage and synchronization of subsystems that develop in different time scales. The relevant techniques applied here are related to a singular perturbation theory for differential systems. A more complicated issue arises for uncertain systems described by differential inclusions, for which an appropriate theory is being developed. In order to make the theory constructive, some further steps are necessary. These are presented in this paper, where a computer-implementable "ellipsoidal" version is given. The results are particularly relevant to the linkage of models related to environmental, demographic and economic problems