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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 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.