Diagnosis of uncertain linear systems: an interval approach

When modelling a physical process, there are always discreapencies between the modelled and real behaviours due to simplifications and neglected effects. Moreover, the parameters of the real process are never rigorously constant and may vary all along the time around a mean value. Thus the process state estimation will strongly depend on these variations which are unknown and thus may be considered as uncertainties. In order to obtain a guaranteed state reconstruction, the influence of these uncertainties have to be taken into account. An adapted representation allowing state reconstruction is the interval model approach which consists in providing a nominal model of the process influenced by uncertainties assumed to be represented by intervals with known bounds. The paper shows how state estimation may be obtained by using interval model approach; based on interval analysis, a set of state estimates is defined which is consistent with the available information (models, measurements, bounded uncertainties).