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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 201432, 11 pages
Research Article

Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Received 28 December 2012; Revised 23 February 2013; Accepted 23 February 2013

Academic Editor: Baocang Ding

Copyright © 2013 Xingjian Wang and Shaoping Wang. 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.


Practical nonlinear systems can usually be represented by partly linearizable models with unknown nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive fuzzy robust control (AFRC) algorithm for such systems. The AFRC effectively combines techniques of adaptive control and fuzzy control, and it improves the performance by retaining the advantages of both methods. The linearizable part will be linearly parameterized with unknown but constant parameters, and the discontinuous-projection-based adaptive control law is used to compensate these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities. Robust control law ensures the robustness of closed-loop control system. A systematic design procedure of the AFRC algorithm by combining the backstepping technique and small-gain approach is presented. Then the closed-loop stability is studied by using small gain theorem, and the result indicates that the closed-loop system is semiglobally uniformly ultimately bounded.