Set-Invariant Estimators for Linear Systems Subject to Disturbances and Measurement Noise

The concept of set-invariance is applied to the design of full-order state observers with limitation of the estimation error, for discrete-time linear systems subject to unknown but bounded persistent disturbances and measurement noise. It is shown that if the initial error belongs to a D-(C,A)-invariant set, then it can be kept in this set by means of a suitable output injection, for all admissible disturbancesand noise. Polyhedral D-(C,A)-invariant sets are explicitly characterized by necessary and sufficient conditions. Based on such conditions, algorithms are proposed for the computation of a D-(C,A)-invariant polyhedron containing the one to which the initial error belongs. The results are illustrated and compared to other approaches by means of a numerical example.