Quadratically convex combination approach to stability of T–S fuzzy systems with time-varying delay

This paper develops a novel stability analysis method for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T–S fuzzy systems are derived by the newly proposed augmented Lyapunov–Krasovski...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2014-07, Vol.351 (7), p.3752-3765
Main Authors: Yang, Feisheng, Guan, Shouping, Wang, Dianhui
Format: Article
Language:English
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Summary:This paper develops a novel stability analysis method for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T–S fuzzy systems are derived by the newly proposed augmented Lyapunov–Krasovski (L–K) functional. This functional contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Different from previous results, our derivation applies the idea of second-order convex combination, and the property of quadratic convex function without resorting to the Jensen's inequality. Two numerical examples are provided to verify the effectiveness of the presented results.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2013.01.025