Set-membership observer design based on ellipsoidal invariant sets

Abstract

Abstract This paper presents a new set-membership observer design method for linear discrete-time systems. The real process is assumed to be perturbed by unknown but bounded disturbances. The set-membership observer provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation errors bounds. The proposed approach is based on the solutions of a few number of Linear Matrix Inequalities that are suitable modified to provide both the observer parameters and ellipsoidal Robustly Positive Invariant sets. The latter are used to frame the estimation error in a very simple and accurate way. The enhanced precision on the computation of the estimation error bounds has been possible thanks to the use of the a posteriori calculated covariance matrix that allows, in a second time, a more suitable description of the dissipation equation used in the Bounded-real lemma formulation. A numerical example illustrates the behavior of such observer and discuss its easy implementation.