Augmented Lyapunov--Krasovskii functional approaches to robust stability criteria for uncertain Takagi--Sugeno fuzzy systems with time-varying delays

Authors:
O. M. Kwon;M. J. Park;S. M. Lee;Ju H. Park
Affiliations:
School of Electrical Engineering, Chungbuk National University, 52 Naesudong-ro, Heungduk-gu, Cheongju 361-763, Republic of Korea;School of Electrical Engineering, Chungbuk National University, 52 Naesudong-ro, Heungduk-gu, Cheongju 361-763, Republic of Korea;School of Electronics Engineering, Daegu University, Jinryang-eup, Gyeongsan 712-714, Republic of Korea;Department of Electrical Engineering, Yeungnam University, 214-1 Dae-dong, Kyongsan 712-749, Republic of Korea
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

This paper considers the problem of robust stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing an augmented Lyapunov-Krasovskii functional and utilizing Finsler's Lemma, a novel criterion for delay-dependent robust stability of T-S fuzzy model with time-varying delay is derived in terms of linear matrix inequalities (LMIs). Also, a further improved stability criterion is proposed by utilizing free weighting techniques. Finally, three numerical examples are included to show the superiority of the proposed criteria.