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Mathematical Problems in Engineering
Volume 2013, Article ID 159279, 12 pages
Research Article

Robust and Passive Constrained Fuzzy Control for Discrete Fuzzy Systems with Multiplicative Noises and Interval Time Delay

1Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan
2School of Naval Architecture and Marine Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China

Received 18 August 2013; Accepted 1 November 2013

Academic Editor: Baoyong Zhang

Copyright © 2013 Wen-Jer Chang 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.


The passive fuzzy control for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy models with multiplicative noises and time delay is investigated subject to robust asymptotical stability. Applying Jensen’s inequality and free-weighting matrix technique, less conservative sufficient conditions are derived via choosing Lyapunov function to analyze and synthesize the robust asymptotical stability and passivity of closed-loop system. The derived conditions are not strictly linear matrix inequality (LMI) problems, thus the cone complementarity technique is employed to propose a suboptimal technique to solve the proposed nonstrictly LMI problems. An algorithm is developed in this paper to design the fuzzy controller which can be accomplished by state-feedback scheme or output-feedback scheme. Finally, numerical examples are provided to demonstrate the feasibility and applicability of the proposed fuzzy controller design technique.