Partial and Full Order Interval Unknown Input State Estimators

In this contribution, interval extensions for both full-order and reduced-order unknown input observers are proposed for uncertain discrete time linear systems. The introduced interval estimators do not rely on the positive systems property of the estimation errors. They are mainly based on numerical schemes conceived to characterize in a rigorous way the reached set of some classes of uncertain dynamical systems. Thus, only the classical existence conditions of unknown input observers are needed to design their interval extensions. Interval analysis is used as a convenient tool to implement the proposed state estimation algorithms. However, other bounded geometrical sets could be also applied. Numerical examples are studied to highlight the effectiveness of the introduced interval estimators in the presence of both system’s uncertainties and unknown inputs.