Novel stability and stabilization criteria for Takagi–Sugeno fuzzy time-delay systems

doi:10.1088/1674-1056/21/3/030204

Abstract We study the problems of stability and stabilization for Takagi-Sugeno (T-S) fuzzy time-delay systems. First, by constructing a less-redundant Lyapunov-Krasovskii function and introducing a useful inequality, an innovative stability criterion is obtained, which gives a significant improvement on the performance. Compared with the exiting references, our result can use fewer unknown variables and get better results. Furthermore, based on the derived stability criteria, a new stabilization condition is developed, in which the controller gain and the maximum allowable delay bound can be obtained simultaneously. The conditions are all derived in the form of linear matrix inequality, which are easy to verify. Finally, numerical examples are given to show the effectiveness of the proposed methods.

Keywords: stabilization free-weighting matrix

Received: 28 May 2011
Revised: 02 November 2011
Accepted manuscript online:

PACS:	02.30.Yy	(Control theory)
	02.60.Cb	(Numerical simulation; solution of equations)
	87.16.A-	(Theory, modeling, and simulations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 61034005, and 61104021), the National High Technology Research and Development Program of China (Grant No. 2009AA04Z127), and the National Basic Research Program of China (Grant No. 2009CB320601).

Corresponding Authors: Gong Da-Wei,pzhzhx@126.com
E-mail: pzhzhx@126.com

Cite this article:

Gong Da-Wei(宫大为), Zhang Hua-Guang(张化光), and Wang Zhan-Shan(王占山) Novel stability and stabilization criteria for Takagi–Sugeno fuzzy time-delay systems 2012 Chin. Phys. B 21 030204

[1]	Takagi T and Sugeno M 1985 IEEE Tran. Syst. Man. Cybernt. 15 116
[2]	Wang H, Tanaka K and Griffin M 1996 it IEEE Transations on Fuzzy Systems 4 14
[3]	Tanaka K, Ikeda T and Wang H 1996 IEEE Transations on Fuzzy Systems 4 1
[4]	Zhang H, Lun S and Liu D 2007 it IEEE Transations on Fuzzy Systems 15 453
[5]	Kim E and Lee H 2000 IEEE Transations on Fuzzy Systems 8 523
[6]	Liu X and Zhang Q 2003 Automatica 39 1571
[7]	Lu J G 2005 Chin. Phys. B 14 703
[8]	Fang C, Liu Y, Kau S, Lin H and Lee C 2006 IEEE Transations on Fuzzy Systems 14 386
[9]	Zhang H, Xie X and Wang X 2010 Chin. Phys. B 19 060504
[10]	Zamania I, Sadati N and Zarif M 2011 Fuzzy Sets and Systems 174 31
[11]	Zhang H and Xie X 2011 IEEE Transations on Fuzzy Systems 19 478
[12]	Ma D Z, Zhang H G, Wang Z S and Feng J 2010 Chin. Phys. B 19 050506
[13]	Lendek Z, Babuvska R and Schutter B 2011 Fuzzy Sets and Systems 174 1
[14]	Cao Y and Frank P M 2001 it Fuzzy Sets and Systems 124 213
[15]	Guan X and Chen C 2004 IEEE Transations on Fuzzy Systems 12 236
[16]	Yoneyama J 2007 Fuzzy Sets and Systems 158 2225
[17]	Wu H and Li H 2007 IEEE Transations on Fuzzy Systems 15 482
[18]	Liu F, Wu M, He Y and Yokoyama R 2010 Fuzzy Sets and Systems 161 2033
[19]	Peng C, Yue D, Yang T C and Tian E G 2009 IEEE Transations on Fuzzy Systems 17 1143
[20]	Hsiao F H 2010 Fuzzy Sets and Systems 161 2760
[21]	Lien C H 2006 Chaos Soliton. Fract. 28 422
[22]	Chen B and Liu X P 2005 IEEE Transations on Fuzzy Systems 13 544
[23]	Guan X P and Chen C L 2004 IEEE Transations on Fuzzy Systems 12 236
[24]	Wu H N and Li H X 2007 IEEE Transations on Fuzzy Systems 15 482
[25]	Zhang X M, Wu M, She J H and He Y 2005 Automatica 41 1405
[26]	Li C G, Wang H J and Liao X F 2004 IET Control Theory and Applications 151 417
[27]	Tian E G and Peng C 2006 Fuzzy Sets and Systems 157 544
[28]	Chen B, Liu X P and Tong S C 2007 Fuzzy Sets and Systems 158 2209
[29]	Wu H N and Li H X 2007 Fuzzy Sets and Systems 15 482
[30]	Lien C, Yu K, Chen W, Wan Z and Chung Y 2007 IET Control Theory and Applications 1 764

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Novel stability and stabilization criteria for Takagi–Sugeno fuzzy time-delay systems

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