Abstract
This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with timevarying delay by delay-partitioning approach and Free-Matrix-based integral inequality. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then, on the basis of taking into account the independent upper bounds of the delay derivative in various delay intervals, some new results on tighter bounding inequalities, such as Peng-Park’s integral inequality and the Free-Matrix-based integral inequality are employed to effectively reduce the enlargement in bounding the derivative of LKF, therefore, less conservative results can be expected in terms of e s and LMIs. Finally, three numerical examples are included to show that the proposed method is less conservative than existing ones.
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Recommended by Associate Editor Tae-Hyoung Kim under the direction of Editor Zengqi Sun. This work was partially supported by the National Natural Science Foundation of China (Grant nos. 11501390, 11501392), the Key Natural Science Foundation of Sichuan Province Education Department (Grant No. 15ZA0234), the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (Grant nos. 2014QZJ02, 2015QZJ02) and the scientific research fund project of SUSE (Grant no. 2012KY09). The authors would like to thank the editor and the anonymous reviewers for their constructive comments and suggestions to improve the quality of the paper.
Wen-Pin Luo received the B.S. degree from Sichuan Normal University, Chengdu, China, in 2004 and the M.S. degree from University of Electronic Science and Technology of China, Chengdu, China, in 2007, all in Applied Mathematics. She is currently a Lecturer with Sichuan University of Science and Engineering, Zigong, China. Her current research interests include fuzzy control systems, impulsive systems and neural networks.
Jun Yang received the B.S. degree from Leshan Normal University, Leshan, China, in 2004 and the Ph.D. degree from University of Electronic Science and Technology of China, Chengdu, China, in 2009, all in Applied Mathematics. He is currently an Associate Professor with Civil Aviation Flight University of China, Guanghan, China. His current research interests include system and control theory, fuzzy control systems and functional differential equations. He is an active reviewer for many international journals.
Xin Zhao received the Ph.D. degree from Sichuan University, Chengdu, China, in 2009, majored in Material Physics and Chemistry. He is currently an Associate Professor with Civil Aviation Flight University of China (CAFUC). His current research interests include aeronautic structural materials and optoelectronic information materials, etc.
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Luo, WP., Yang, J. & Zhao, X. Free-matrix-based integral inequality for stability analysis of uncertain T-S fuzzy systems with time-varying delay. Int. J. Control Autom. Syst. 14, 948–956 (2016). https://doi.org/10.1007/s12555-015-0228-3
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DOI: https://doi.org/10.1007/s12555-015-0228-3