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Mathematical Problems in Engineering
Volume 2013, Article ID 913234, 14 pages
Research Article

Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

1Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, China
2Faculty of Engineering and Science, University of Agder, N-4898 Grimstad, Norway

Received 29 November 2012; Accepted 27 December 2012

Academic Editor: M. Chadli

Copyright © 2013 Zhixiong Zhong 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 stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.