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Mathematical Problems in Engineering
Volume 2013, Article ID 215201, 12 pages
Research Article

Observer-Based Robust Adaptive Fuzzy Control for MIMO Nonlinear Uncertain Systems with Delayed Output

Department of Electrical Engineering, Tatung University, 40 Chung-Shan North Road, Sec. 3, Taipei, Taiwan

Received 29 October 2012; Revised 20 January 2013; Accepted 22 January 2013

Academic Editor: Peng Shi

Copyright © 2013 Chiang Cheng Chiang. 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.


An observer-based robust adaptive fuzzy control scheme is presented to tackle the problem of the robust stability and the tracking control for a class of multiinput multioutput (MIMO) nonlinear uncertain systems with delayed output. Because the nonlinear system functions and the uncertainties of the controlled system including structural uncertainties are supposed to be unknown, fuzzy logic systems are utilized to approximate these nonlinear system functions and the upper bounded functions of the uncertainties. Moreover, the upper bound of uncertainties caused by these fuzzy modeling errors is also estimated. In addition, the state observer based on state variable filters is designed to estimate all states which are not available for measurement in the controlled system. By constructing an appropriate Lyapunov function and using strictly positive-real (SPR) stability theorem, the proposed robust adaptive fuzzy controller not only guarantees the robust stability of a class of multivariable nonlinear uncertain systems with delayed output but also maintains a good tracking performance. Finally, some simulation results are illustrated to verify the effectiveness of the proposed control approach.