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Mathematical Problems in Engineering
Volume 2017, Article ID 9251031, 12 pages
Research Article

Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

National Higher School of Engineering of Tunis (ENSIT), Laboratoire d’Ingenierie des Systèmes Industriels et des Energies Renouvelables (LISIER), University of Tunis, 5 Taha Hussein Street, BP 56, 1008 Tunis, Tunisia

Correspondence should be addressed to Feten Gannouni; rf.oohay@inuonnagnetef

Received 30 July 2016; Revised 8 October 2016; Accepted 24 October 2016; Published 15 January 2017

Academic Editor: Alberto Borboni

Copyright © 2017 Feten Gannouni and Fayçal Ben Hmida. 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.


We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.