Interval observer design for discrete linear time-invariant systems with uncertainties

This paper considers the problem of constructing an interval observer for systems described by discrete-time linear models under uncertainties in the form of exogenous disturbances and measurement noise (unknown bounded functions). Such an observer is designed using the minimal-dimension model of the original system invariant with respect to the disturbances. The dynamic matrix of this model is defined in the identification canonical form. We present relations to design an interval observer of minimal complexity for estimating the set of admissible values of a given linear function of the state vector. If the observer invariant with respect to the disturbances does not exist, we suggest a method to construct an observer with minimal sensitivity to them based on the singular value decomposition of system matrices. Theoretical results are illustrated by an example.