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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 3918797, 11 pages
Research Article

Extended Ellipsoidal Outer-Bounding Set-Membership Estimation for Nonlinear Discrete-Time Systems with Unknown-but-Bounded Disturbances

School of Instrumentation Science and Opto-Electronics Engineering, Beihang University (BUAA), Beijing 100191, China

Received 15 February 2016; Accepted 5 April 2016

Academic Editor: Driss Boutat

Copyright © 2016 Yushuang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops an extended ellipsoidal outer-bounding set-membership estimation (EEOB-SME) algorithm with high accuracy and efficiency for nonlinear discrete-time systems under unknown-but-bounded (UBB) disturbances. The EEOB-SME linearizes the first-order terms about the current state estimations and bounds the linearization errors by ellipsoids using interval analysis for nonlinear equations of process and measurement equations, respectively. It has been demonstrated that the EEOB-SME algorithm is stable and the estimation errors of the EEOB-SME are bounded when the nonlinear system is observable. The EEOB-SME decreases the computation load and the feasible sets of EEOB-SME contain more true states. The efficiency of the EEOB-SME algorithm has been shown by a numerical simulation under UBB disturbances.