Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

doi:10.1088/1674-1056/23/4/040701

Abstract This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional (2D) systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.

Keywords: stability analysis Roesser-type two-dimensional system slack matrix variable reducing conservatism

Received: 30 July 2013
Revised: 04 September 2013
Accepted manuscript online:

PACS:

07.05.Mh

(Neural networks, fuzzy logic, artificial intelligence)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61203057 and 51305066).

Corresponding Authors: Dai Xiao-Lin
E-mail: www_dxl@126.com,xldai_uest@163.com

About author: 07.05.Mh

Cite this article:

Dai Xiao-Lin (代小林) Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems 2014 Chin. Phys. B 23 040701

[1]	Roesser R P 1975 IEEE Transactions on Automatic Control 20 1
[2]	Fornasini E and Marchesini G 1976 IEEE Transactions on Automatic Control 21 484
[3]	Owens D H, Amann N, Rogers E and French M 2000 Multidimensional Systems and Signal Processing 11 125
[4]	Sulikowski B, Galkowski K, Rogers E and Owens D H 2004 Automatica 40 2167
[5]	Sulikowski B, Galkowski K, Rogers E and Owens D H 2006 Automatica 42 877
[6]	Xu J M and Yu L 2008 Automatica 44 809
[7]	Wu L G, Shi P, Gao H J and Wang C H 2008 Automatica 44 1849
[8]	Singh V 2008 IEEE Transactions on Circuits and Systems II: Express Briefs 55 793
[9]	Li D, Wang H, Yang D, Zhang X H and Wang S L 2008 Chin. Phys. B 17 4091
[10]	Zhao Y, Zhang H G and Zheng C D 2008 Chin. Phys. B 17 529
[11]	Zhang H G, Zhao Y, Yu W and Yang D S 2008 Chin. Phys. B 17 4056
[12]	Zhang H G, Xie X P and Wang X Y 2010 Chin. Phys. B 19 060504
[13]	Feng Y F and Zhang Q L 2011 Chin. Phys. B 20 010101
[14]	Feng Y F, Zhang Q L and Feng D Z 2012 Chin. Phys. B 21 100701
[15]	Gong D W, Zhang H G and Wang Z S 2012 Chin. Phys. B 21 030204
[16]	Kim E and Lee H 2000 IEEE Transactions on Fuzzy Syetems 8 523
[17]	Sala A and Arino C 2007 Fuzzy Sets and Systems 24 2671
[18]	Montagner V F, Oliveira R and Peres P 2009 IEEE Transactions on Fuzzy Syetems 17 863
[19]	Xie X P, Ma H J, Zhao Y, Ding D W and Wang Y C 2013 IEEE Transactions on Fuzzy Systems 21 147
[20]	Kruszewski A, Wang R and Guerra T M 2008 IEEE Transactions on Automatic Control 53 606
[21]	Zhang H G, Xie X P and Tong S C 2011 IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics 41 1313
[22]	Zhang H G and Xie X P 2011 IEEE Transactions on Fuzzy Systems 19 478
[23]	Zhang T Y, Zhao Y and Xie X P 2012 Chin. Phys. B 21 120503
[24]	Kar H and Singh V 1997 IEEE Transactions on Signal Processing 45 2620
[25]	Kokil P, Dey A and Kar H 2012 Signal Processing 92 2874
[26]	Singh V 2012 Digital Signal Processing 22 471

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