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Journal of Applied Mathematics
Volume 2013, Article ID 714525, 10 pages
Research Article

Passivity and Passification for Delay Fuzzy System Based on Delay Partitioning Approach

1The State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
2Department of Automation, North China Electric Power University, Baoding 071003, China

Received 17 February 2013; Accepted 28 March 2013

Academic Editor: Constantinos Siettos

Copyright © 2013 Xiangjie Liu 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.


A delay partitioning approach is introduced to solve problems of passivity and passification for continuous T-S fuzzy system with time delay. Our aim is to design a state feedback controller such that the resulting closed system is passive. By constructing a Lyapunov-Krasovskii functional, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities (LMIs). Finally, numerical examples are used to illustrate the effectiveness of the proposed approaches which can further reduce conservatism and become more obvious with partitioning getting thinner.