Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

doi:10.1088/1674-1056/22/3/030206

Abstract We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional (2D) systems. The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model, and the uncertainty phenomenon, which appears typically in practical environments, is modeled by a convex bounded (polytope type) uncertain domain. Then, the stability analysis and control synthesis of uncertain discrete-time 2D systems are developed by applying the Lyapunov stability theory. In the processes of stability analysis and control synthesis, the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques. Moreover, the obtained results are formulated in the form of linear matrix inequalities, which can be easily solved via the standard numerical software. Finally, numerical examples are given to demonstrate the effectiveness of the obtained results.

Keywords: uncertain two-dimensional systems Roesser model Lyapunov stability theory control synthesis

Received: 06 August 2012
Revised: 05 September 2012
Accepted manuscript online:

PACS:	02.30.Yy	(Control theory)
	02.30.-f	(Function theory, analysis)
	02.40.Ft	(Convex sets and geometric inequalities)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61104010).

Corresponding Authors: Wang Jia
E-mail: wangjiasackville@163.com

Cite this article:

Wang Jia (王佳), Hui Guo-Tao (会国涛), Xie Xiang-Peng (解相朋) Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems 2013 Chin. Phys. B 22 030206

[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 Acta Automatica Sinica 34 809
[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]	Jin X Z and Yang G H 2010 Chin. Phys. B 19 080508
[10]	Syed A M 2011 Chin. Phys. B 20 080201
[11]	Ma T D, Zhang H G and Fu J 2008 Chin. Phys. B 17 4407
[12]	Chen D L and Zhang W D 2008 Chin. Phys. B 17 1506
[13]	Feng Y F and Zhang Q L 2010 Chin. Phys. B 19 120504
[14]	Feng Y F and Zhang Q L 2011 Chin. Phys. B 20 010101
[15]	Syed A M 2012 Chin. Phys. B 21 070207
[16]	Li D, Wang S L, Zhang X H and Yang D 2010 Chin. Phys. B 19 010506
[17]	Gao T F, Liu F S and Chen J C 2012 Chin. Phys. B 21 020502
[18]	Zhang H G, Xie X P and Wang X Y 2010 Chin. Phys. B 19 060504
[19]	Xu W, Ao P and Yuan B 2011 Chin. Phys. Lett. 28 050201
[20]	Fu J and Ma T D 2011 Chin. Phys. B 20 050511
[21]	Guo Y, Qu Z H and Tang W Y 2011 Chin. Phys. Lett. 28 110204
[22]	Geromel J C, Oliveira M C and Hsu L 1998 Linear Algebra and Its Applications 285 69
[23]	Gahinet P, Apkarian P and Chilali M 1996 IEEE Transactions on Automatic Control 41 436
[24]	Oliveira R and Peres P 2009 Automatica 45 2620
[25]	Zhang H G and Xie X P 2011 IEEE Transactions on Fuzzy Systems 19 478
[26]	Chesi G 2010 IEEE Transactions on Automatic Control 55 2500
[27]	Xie X P, Ma H J, Zhao Y, Ding D W and Wang Y C 2012 IEEE Transactions on Fuzzy Systems 20 1
[28]	Balini H, Witte J and Scherer W 2012 Automatica 48 521
[29]	Zhang H G, Xie X P and Tong S C 2011 IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics 41 1313
[30]	Singh V 2012 Signal Processing 92 240
[31]	De Oliveira J V, Bernussou J and Geromel J C 1999 Systems & Control Letters 37 261
[32]	Xie X P and Zhang H G 2010 Acta Automatica Sinica 36 267

[1]	Chaotic synchronization in Bose–Einstein condensate of moving optical lattices via linear coupling Zhang Zhi-Ying (张志颖), Feng Xiu-Qin (冯秀琴), Yao Zhi-Hai (姚治海), Jia Hong-Yang (贾洪洋). Chin. Phys. B, 2015, 24(11): 110503.
[2]	Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique Zhang Tie-Yan (张铁岩), Zhao Yan (赵琰), Xie Xiang-Peng (解相朋). Chin. Phys. B, 2012, 21(12): 120503.
[3]	Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions Dai Hao (戴浩), Jia Li-Xin (贾立新), Zhang Yan-Bin (张彦斌). Chin. Phys. B, 2012, 21(12): 120508.
[4]	Global exponential synchronization between Lü system and Chen system with unknown parameters and channel time-delay Ma Tie-Dong (马铁东), Fu Jie (浮洁). Chin. Phys. B, 2011, 20(5): 050511.
[5]	A new three-dimensional chaotic system and its modified generalized projective synchronization Dai Hao(戴浩), Jia Li-Xin(贾立新), Hui Meng(惠萌), and Si Gang-Quan(司刚全) . Chin. Phys. B, 2011, 20(4): 040507.
[6]	A new four-dimensional hyperchaotic Lorenz system and its adaptive control Si Gang-Quan(司刚全), Cao Hui(曹晖), and Zhang Yan-Bin(张彦斌). Chin. Phys. B, 2011, 20(1): 010509.
[7]	Projective synchronization of spatiotemporal chaos in a weighted complex network Lü Ling(吕翎), Chai Yuan(柴元), and Luan Ling(栾玲). Chin. Phys. B, 2010, 19(8): 080506.
[8]	Generalized chaos synchronization of a weighted complex network with different nodes Lü Ling(吕翎), Li Gang(李钢), Guo Li(郭丽), Meng Le(孟乐),Zou Jia-Rui(邹家蕊), and Yang Ming(杨明). Chin. Phys. B, 2010, 19(8): 080507.
[9]	$\mathscr{L}$₂–$\mathscr{L}$_$\infty$ learning of dynamic neural networks Choon Ki Ahn. Chin. Phys. B, 2010, 19(10): 100201.
[10]	A new four-dimensional hyperchaotic Chen system and its generalized synchronization Jia Li-Xin(贾立新), Dai Hao(戴浩), and Hui Meng(惠萌). Chin. Phys. B, 2010, 19(10): 100501.
[11]	Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system Cai Guo-Liang(蔡国梁), Zheng Song(郑松), and Tian Li-Xin(田立新) . Chin. Phys. B, 2008, 17(7): 2412-2419.
[12]	Adaptive synchronization of a critical chaotic system Tu Li-Lan (涂俐兰), Lu Jun-An (陆君安). Chin. Phys. B, 2005, 14(9): 1755-1759.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

Cite this article:

Online attention