New delay-dependent stability analysis and synthesis of T-S fuzzy systems with time-varying delay

In this paper, a new method is proposed for stability analysis and synthesis of Takagi–Sugeno (T–S) fuzzy systems with time‐varying delay. Based on a new Lyapunov–Krasovskii functional (LKF), some less conservative delay‐dependent stability criteria are established. In the derivation process, some a...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2010-02, Vol.20 (3), p.313-322
Main Authors: Yang, Zhong, Yang, Yu-Pu
Format: Article
Language:English
Subjects:
Criteria
Delay
delay-dependent
Derivatives
free-weighting matrices
fuzzy control
Fuzzy systems
linear matrix inequality (LMI)
Mathematical models
Stability
Stability analysis
Synthesis
time-varying delay
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Summary:In this paper, a new method is proposed for stability analysis and synthesis of Takagi–Sugeno (T–S) fuzzy systems with time‐varying delay. Based on a new Lyapunov–Krasovskii functional (LKF), some less conservative delay‐dependent stability criteria are established. In the derivation process, some additional useful terms, ignored in previous methods, are considered and new free‐weighting matrices are introduced to estimate the upper bound of the derivative of LKF for T–S fuzzy systems with time‐varying delay. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
1099-1239
DOI:10.1002/rnc.1431