Improved delay-dependent robust H∞ control of an uncertain stochastic system with interval time-varying and distributed delays

doi:10.1088/1674-1056/23/12/120201

›› 2014, Vol. 23 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/23/12/120201

• GENERAL • 下一篇

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

M. Syed Ali, R. Saravanakumar

Department of Mathematics Thiruvalluvar University, Vellore-632115, Tamil Nadu, India

收稿日期:2014-02-13 修回日期:2014-07-09 出版日期:2014-12-15 发布日期:2014-12-15
基金资助:
Project supported by the Fund from the Department of Science and Technology (DST) (Grant No. SR/FTP/MS-039/2011).

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

M. Syed Ali, R. Saravanakumar

Department of Mathematics Thiruvalluvar University, Vellore-632115, Tamil Nadu, India

Received:2014-02-13 Revised:2014-07-09 Online:2014-12-15 Published:2014-12-15
Contact: M. Syed Ali E-mail:syedgru@gmail.com
Supported by:
Project supported by the Fund from the Department of Science and Technology (DST) (Grant No. SR/FTP/MS-039/2011).

摘要/Abstract

摘要： In this paper, the robust H_∞ control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying, and distributed delay. The aim is to design a delay-dependent robust H_∞ control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

关键词: distributed delay, interval time-varying delay, H_∞ control, linear matrix inequality (LMI), stochastic systems

Abstract: In this paper, the robust H_∞ control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying, and distributed delay. The aim is to design a delay-dependent robust H_∞ control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

Key words: distributed delay, interval time-varying delay, H_∞ control, linear matrix inequality (LMI), stochastic systems

中图分类号: (Ordinary differential equations)

02.30.Hq

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.40.Jc (Brownian motion) 02.30.Yy (Control theory)

M. Syed Ali, R. Saravanakumar. Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays[J]. , 2014, 23(12): 120201-120201.

M. Syed Ali, R. Saravanakumar. Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays[J]. Chin. Phys. B, 2014, 23(12): 120201-120201.

参考文献 50

[1]	Syed Ali M and Balasubramaniam P 2010 Int. J. Comput. Math. 87 1363
[2]	Syed Ali M and Balasubramaniam P 2009 Expert Systems with Applications 36 10583
[3]	Kim JH and Park HB 1999 Automatica 35 1443
[4]	Liu P L 2011 Int. J. Gen. Syst. 40 301
[5]	Li L and Liu X 2009 Inform. Sci. 179 1134
[6]	Li X and Souza C E D 1997 IEEE Trans. Automat. Control 42 1144
[7]	Jiang X and Han Q L 2007 Fuzzy Syst. 15 321
[8]	Zhu X L Wang X L and Yang G H 2010 IET Control Theory Appl. 4 1101
[9]	Jiang X and Han Q L 2005 Automatica 41 2099
[10]	Song X, Xu S and Shen H 2008 Inform. Sci. 178 4341
[11]	Xu S and Chen T 2004 IEEE Trans. Circuits Syst. II 51 195
[12]	Xu S, Lam J, Chen T and Zou Y 2005 IEEE Trans. Signal Process. 53 3764
[13]	Kwon O M, Park M J and Park J H 2012 J. Franklin Inst. 349 2799
[14]	Lakshmanan S, Senthilkumar T and Balasubramaniam P 2011 Appl. Math. Model. 35 5355
[15]	Balasubramaniam P and Lakshmanan S 2009 Nonlinear Anal. Hybrid Systems 3 749
[16]	Balasubramaniam P and Nagamani G 2012 Expert Systems with Applications 39 732
[17]	Balasubramaniam P, Krishnasamy R and Rakkiyappan R 2011 Nonlinear Anal. Hybrid Systems 5 681
[18]	Gu K, Kharitonov V L and Chen J 2003 Stability of Time-Delay Systems (Boston: Birkhuser)
[19]	Gorecki H, Fuksa S, Grabowski P and Korytowski A 1989 Analysis and Synthesis of Time Delay Systems (New York: John Wiley and Sons)
[20]	Kolmanovskii V B and Shaikhet L E 1996 Control of Systems with After Effect (Am. Math. Soc.: USA)
[21]	Zheng F and Frank P M 2002 Automatica 38 487
[22]	Zames G 1981 IEEE Trans. Automat. Control 26 301
[23]	Peng C and Tian YC 2009 Inform. Sci. 179 3187
[24]	Cao Y and Lam J 2003 J. Franklin Inst. 340 423
[25]	Senthilkumar T and Balasubramaniam P 2011 Appl. Math. Lett. 24 1986
[26]	Shi P, Xu S Y, Chu Y M and Zou Y 2006 J. Math. Anal. Appl. 314 1
[27]	Wen S, Zeng Z, Huang T and Bao G 2013 ISA Transactions 52 207
[28]	Costa O and Benites G 2011 Automatica 47 466
[29]	Xu S and Chen T 2002 IEEE Trans. Automat. Control 47 2089
[30]	Lin X Y, Zhang W H and Wang X R 2009 Acta Math. Appl. Sin. 32 476
[31]	Xu S Y and Chen T 2004 Automatica 40 2091
[32]	Lu H Q and Zhou W N 2009 Control Decis. 24 76
[33]	Ma S and Zhang C 2009 Int. J. Robust Nonlinear Control 19 965
[34]	Zhang L and Boukas E K 2008 Int. J. Robust Nonlinear Control 19 868
[35]	Wen S, Zeng Z and Huang T 2012 IEEE Trans. Circuits Syst. II: Exp. Briefs 59 820
[36]	Mao X 2008 Stochastic Differential Equations with Applications (Chichsester: Horwood, U.K.)
[37]	Zheng C D, Shan Q H, Zhang H and Wang Z 2013 IEEE Trans. Neural Netw. Learn. Syst. 24 800
[38]	Wang G, Huang C, Zhang Q and Yang C 2014 IET Control Theory Appl. 8 367
[39]	Wen S P, Zeng Z G, Huang T W and Li C J 2013 Int. J. Robust Nonlinear Control 21 DOI:10.1002/rnc.3112 doi: 10.1002/rnc.3112
[40]	Wu H, Liao X and Feng W 2012 Cogn Neurodyn 6 443
[41]	Syed Ali M and Balasubramaniam P 2008 Phys. Lett. 372 5159
[42]	Syed Ali M and Maruthai M 2011 Math. Comput. Model. 54 1979
[43]	Boyd B, Ghoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadephia: SIAM)
[44]	Gahinet P, Nemirovski A, Laub A and Chilali M 1995 LMI Control Toolbox User's Guide (Natick: The Mathworks)
[45]	Chen B, Liu X and Lin C 2009 Fuzzy Sets and Systems 160 403
[46]	Quan Q, Yang D, Hu H and Cai K Y 2010 Nonlinear Anal. Real World Appl. 11 3752
[47]	Moon Y S, Park P, Kwon W H and Lee Y S 2001 Int. J. Control 74 1447
[48]	Chen W Y 2002 Int. J. Syst. Sci. 33 917
[49]	Jing X J, Tan D L and Wang Y C 2004 IEEE Trans. Automat. Contol 49 1192
[50]	Yan H C, Huang X H, Zhang H and Wang M 2009 Chaos, Solitons and Fractals 40 1668

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 50

相关文章 10

Metrics

本文评价

推荐阅读 0

[1]	R Saravanakumar, M Syed Ali. Robust H_∞ control for uncertain Markovian jump systems with mixed delays[J]. 中国物理B, 2016, 25(7): 70201-070201.
[2]	M. Syed Ali, R. Saravanakumar. Robust H_∞ control of uncertain systems with two additive time-varying delays[J]. 中国物理B, 2015, 24(9): 90202-090202.
[3]	刘伟, 柳爱利, 周绍磊. Distributed H_∞ control of multi-agent systems with directed networks[J]. 中国物理B, 2015, 24(9): 90208-090208.
[4]	M. Syed Ali, R. Saravanakumar. Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays[J]. 中国物理B, 2015, 24(5): 50201-050201.
[5]	M. J. Park, S. M. Lee, J. W. Son, O. M. Kwon, E. J. Cha. Leader–following consensus control for networked multi-teleoperator systems with interval time-varying communication delays[J]. 中国物理B, 2013, 22(7): 70506-070506.
[6]	王健安. Novel delay-dependent stability criteria for neural networks with interval time-varying delay[J]. 中国物理B, 2011, 20(12): 120701-120701.
[7]	姚洪兴, 周佳燕. Global exponential stability of mixed discrete and distributively delayed cellular neural network[J]. 中国物理B, 2011, 20(1): 10701-010701.
[8]	陈狄岚, 张卫东. Nonlinear H_∞ control of structured uncertain stochastic neural networks with discrete and distributed time varying delays[J]. 中国物理B, 2008, 17(4): 1506-1512.
[9]	李东, 王慧, 杨丹, 张小洪, 王时龙. Exponential stability of cellular neural networks with multiple time delays and impulsive effects[J]. 中国物理B, 2008, 17(11): 4091-4099.
[10]	李桂芳, 李会莹, 杨成梧. Observer-based passive control for uncertain linear systems with delay in state and control input[J]. 中国物理B, 2005, 14(12): 2379-2386.