Abstract
This paper focuses on the robust stability criteria of uncertain T-S fuzzy systems with timevarying delay by delay-partitioning approach. An appropriate Lyapunov-Krasovskii functional is established in the framework of state vector augmentation. Then, on the basis of the Finsler’s lemma, some tighter bounding inequalities (Seuret-Wirtinger’s integral inequality and Peng-Park’s integral inequality) are employed to deal with (time-varying) delay-dependent integral items. Therefore, less conservative delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs), which can be solved efficiently with the Matlab LMI toolbox. Finally, two numerical examples are provided to show that the proposed conditions are less conservative than existing ones.
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Recommended by Associate Editor Izumi Masubuchi under the direction of Editor Euntai Kim.
This work was partially supported by the scientific research foundation of CAFUC (J2014-50, Q2010-75), the joint fund of the national natural science and civil aviation research foundation of China (U1333133), the scientific research fund project of SUSE (2012KY09, 2013QZJ02, 2014RC03, 2014QYJ03, 2014PY08) and the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (2014QZJ02). 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. The authors are also deeply indebted to Professor Chen Peng (Nanjing Normal University) and Professor Hong-Bing Zeng (Hunan University of Technology) for their kindhearted help.
Jun Yang received his B.S. degree from Leshan Normal University, Leshan, China, in 2004 and his 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.
Wen-Pin Luo received her B.S. degree from Sichuan Normal University, Chengdu, China, in 2004 and her 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.
Yong-Hu Wang received his Ph.D. degree from Northwestern Polytechnical University (NPU), Xi’an, China, in 2008, majored in Applied Mechanics. He is currently an Associate Professor with Civil Aviation Flight University of China (CAFUC). His current research interests include flight theory and performance, flight quality monitoring, crashworthiness and airworthiness analysis, aircraft ditching and aviation safety, etc.
Chun-Sheng Duan received his B.S. and M.S. degrees from Southwest University, Chongqing, China, in 2000 and 2003, respectively, all in Basic Mathematics. He is currently a Lecturer with Civil Aviation Flight University of China, Guanghan, China. His current research interests include differential geometry and differential equations.
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Yang, J., Luo, WP., Wang, YH. et al. Improved stability criteria for T-S fuzzy systems with time-varying delay by delay-partitioning approach. Int. J. Control Autom. Syst. 13, 1521–1529 (2015). https://doi.org/10.1007/s12555-014-0394-8
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DOI: https://doi.org/10.1007/s12555-014-0394-8