Improved set-membership estimation approach based on zonotopes and ellipsoids

This paper presents an improved approach for guaranteed state estimation combining set-membership estimation techniques based on zonotopes and ellipsoids, applied on linear discrete-time systems with unknown but bounded perturbations and noises. The proposed approach starts with a zonotopic approximation and continues with an ellipsoidal approximation; this allows to manage the trade-off between the accuracy of the zonotopic estimation and the reduced complexity of the ellipsoidal estimation. A new criterion based on the P-radius of a zonotope is proposed to make the transition from the zonotopic estimation to the ellipsoidal estimation. An illustrative example is analyzed to show the advantages of the proposed approach.