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Mathematical Problems in Engineering
Volume 2013, Article ID 724918, 13 pages
Research Article

Control Design for Discrete-Time Fuzzy Systems with Disturbance Inputs via Delta Operator Approach

1College of Information Science and Technology, Bohai University, Jinzhou, Liaoning 121013, China
2College of Engineering, Bohai University, Jinzhou, Liaoning 121013, China
3Department of Engineering of the Faculty of Engineering and Science, University of Agder, Grimstad, Norway

Received 21 August 2013; Accepted 22 September 2013

Academic Editor: Tao Li

Copyright © 2013 Qi Zhou 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.


This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a state-feedback passive controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. The existence conditions of the controller can be expressed by linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method.