Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

doi:10.1088/1674-1056/20/1/010506

中国物理B ›› 2011, Vol. 20 ›› Issue (1): 10506-010506.doi: 10.1088/1674-1056/20/1/010506

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

Ju H. Park¹, S.M. Lee², O.M. Kwon³

(1)Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea; (2)Department of Electronic Engineering, Daegu University, Gyungsan 712-714, Republic of Korea; (3)School of Electrical Engineering, Chungbuk National University, 410 SungBong-Ro, Heungduk-gu, Cheongju 361-763, Republic of Korea

收稿日期:2010-06-25 修回日期:2010-09-27 出版日期:2011-01-15 发布日期:2011-01-15
基金资助:
Project supported by the Daegu University Research (Grant No. 2009).

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

S.M. Lee^a), O.M. Kwon^b), and Ju H. Park^c)^†

^a Department of Electronic Engineering, Daegu University, Gyungsan 712-714, Republic of Korea; ^b School of Electrical Engineering, Chungbuk National University, 410 SungBong-Ro, Heungduk-gu, Cheongju 361-763, Republic of Korea; ^c Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea

Received:2010-06-25 Revised:2010-09-27 Online:2011-01-15 Published:2011-01-15
Supported by:
Project supported by the Daegu University Research (Grant No. 2009).

摘要/Abstract

摘要： In this paper we present a synchronization method for chaotic Lur'e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur'e systems with deadzone nonlinearity. Based on the Lyapunov--Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.

关键词: Lur'e systems, synchronization, deadzone, linear matrix inequality

Abstract: In this paper we present a synchronization method for chaotic Lur'e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur'e systems with deadzone nonlinearity. Based on the Lyapunov–Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.

Key words: Lur'e systems, synchronization, deadzone, linear matrix inequality

中图分类号: (Control of chaos, applications of chaos)

05.45.Gg

S.M. Lee, O.M. Kwon, Ju H. Park. Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity[J]. 中国物理B, 2011, 20(1): 10506-010506.

S.M. Lee, O.M. Kwon, and Ju H. Park . Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity[J]. Chin. Phys. B, 2011, 20(1): 10506-010506.

参考文献 25

[1]	Brown R and Kocarev L 2000 Chaos 10 344
[2]	Hasler H 1994 Synchronization Principles and Applications (Tutorials IEEE-ISCAS'94, Piscataway, NJ) p314
[3]	Chua L O 1994 Int. J. Circuit Theory and App. 22 279
[4]	Suykens J A K and Chua L O 1997 Int. J. Bifurcation and Chaos 7 1873
[5]	Lu J, Han F, Yu X and Chen G 2004 Automatica 40 1677
[6]	Lu J, Yu S, Leung H and Chen G 2006 IEEE Trans. Circuits and Systems-I 53 149
[7]	Lu J and Chen G 2006 Int. J. Bifurcation and Chaos 16 775
[8]	Khalil H K 1996 Nonlinear Systems (2nd Ed.) (Englewnd Cliffs, NJ: Prentice Hall)
[9]	Lur'e A I and Postnikov V N 1944 Prikl. Mat. Meh. 8
[10]	Vidyasagar M 1993 Nonlinear System Analysis (2nd ed) (Englewood Cliffs, NJ: Prentice Hall)
[11]	Pittet C, Tarbouriech S and Burgat C 1997 Proc. 36th IEEE-CDC p4518
[12]	Kapila V, Sparks A G and Pan H 2001 Int. J. Control 74 586
[13]	Hu T, Teel A R and Zaccarian L 2006 IEEE Trans. Automat. Control 51 1770
[14]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
[15]	Yalcin M E, Suykens J A K and Vandewalle J 2001 Int. J. Bifur. Chaos 11 1707
[16]	Liao X and Chen G 2003 Int. J. Bifur. Chaos 13 207
[17]	Cao J, Li H X and Ho D W C 2005 Chaos, Solitons and Fractals 23 1285
[18]	Han Q L 2007 Phys. Lett. A 360 563
[19]	Park Ju H, Lee S M and Kwon O M 2007 Phys. Lett. A 371 263
[20]	Lee S M, Choi S J, Ji D H, Park Ju H and Won S C 2010 wxNonlinear Dynamics59 277
[21]	Li T, Yu J and Wang Z 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 1796
[22]	Kwon O M and Park Ju H 2008 Appl. Math. Comput. 203 813
[23]	Boyd S, Ghaoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia, SIAM)
[24]	Dai D, Hu T, Teel A R and Zaccarian L 2009 Systems and Control Lett. 58 365
[25]	Teel A R and Praly L 2000 Math. Control Signals Systems 13 95

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

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