Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 794581, 21 pages
Research Article

Unknown Input Observer Design for Fuzzy Bilinear System: An LMI Approach

1Laboratoire des Systèmes Avancés (LSA), Polytechnic High School of Tunisia (EPT), University of Carthage, 2078 La Marsa, Tunisia
2University of Picardie-Jules Verne, MIS 33, rue Saint-Leu,- 80039 Amiens, France

Received 8 September 2012; Revised 18 October 2012; Accepted 19 October 2012

Academic Editor: Peng Shi

Copyright © 2012 D. Saoudi 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.


A new method to design a fuzzy bilinear observer (FBO) with unknown inputs is developed for a class of nonlinear systems. The nonlinear system is modeled as a fuzzy bilinear model (FBM). This kind of T-S fuzzy model is especially suitable for a nonlinear system with a bilinear term. The proposed fuzzy bilinear observer subject to unknown inputs is developed to ensure the asymptotic convergence of the error dynamic using the Lyapunov method. The proposed design conditions are given in linear matrix inequality (LMI) formulation. The paper studies also the problem of fault detection and isolation. An unknown input fuzzy bilinear fault diagnosis observer design is proposed. This work is given for both continuous and discrete cases of fuzzy bilinear models. Illustrative examples are chosen to provide the effectiveness of the given methodology.