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Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. (English) Zbl 1239.93043
Summary: In this paper, we investigate the synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Using a combination of Riccati differential equation approach, Lyapunov-Krasovskii functional, and inequality techniques, some sufficient conditions for exponentially stability of the error system are formulated in form of a solution to the standard Riccati differential equation. The designed controller ensures that the synchronization of non-autonomous chaotic systems are proposed via delayed feedback control and intermittent linear state delayed feedback control. Numerical simulations are presented to illustrate the effectiveness of these synchronization criteria.

93B52Feedback control
34H05ODE in connection with control problems
93C15Control systems governed by ODE
Full Text: DOI
[1] Botmart, T.; Niamsup, P.: Adaptive control and synchronization perturbed chuas system, Math comput simulat 75, 37-55 (2007) · Zbl 1115.37072 · doi:10.1016/j.matcom.2006.08.008
[2] Cai, J.; Wu, X.; Chen, S.: Synchronization criteria for non-autonomous chaotic systems with sinusoidal state error feedback control, Phys scr 75, 379-387 (2007) · Zbl 1130.93361 · doi:10.1088/0031-8949/75/3/025
[3] Cao, J.; Ho, D. W. C.; Yang, Y.: Prolective synchronization of a class of delayed chaotic systems via impulsive control, Phys lett A 373, 3128-3133 (2009) · Zbl 1233.34017 · doi:10.1016/j.physleta.2009.06.056
[4] Cao, J.; Wang, Z.; Sun, Y.: Synchronization in an array of linearly stochastically coupled networks with time delays, Phys A 385, 718-728 (2007)
[5] Carroll, T. L.; Pecora, L. M.: Synchronizing non-autonomous chaotic circuits, IEEE trans circuits syst II 40, 646-650 (1993)
[6] Chen, H. K.: Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping, J sound vibration 255, 719-740 (2002) · Zbl 1237.70094
[7] Diecy, L.: On the numerical solution of differential and algebraic Riccati equations, and related matters, (1990)
[8] Ge, Z. M.; Lee, J. K.: Chaos synchronization and parameter identification for gyroscope system, Appl math comput 163, 667-682 (2005) · Zbl 1116.70012 · doi:10.1016/j.amc.2004.04.008
[9] Ge, Z. M.; Yu, T. C.; Chen, Y. S.: Chaos synchronization of a horizontal platform system, J sound vibration 268, 731-749 (2003)
[10] Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay system, (2003) · Zbl 1039.34067
[11] Guo, H.; Zhong, S.: Synchronization criteria of time-delay feedback control system with sector-bounded nonlinearity, Appl math comput 191, 550-559 (2007) · Zbl 1193.93144 · doi:10.1016/j.amc.2007.02.154
[12] Hale, J. K.; Lunee, S. M. Verduyn: Introduction to functional differential equations, (1993)
[13] He, W.; Cao, J.: Generalized synchronization of chaotic systems: an auxiliary system approach via matrix measure, Chaos 19, 013118 (2009) · Zbl 1311.34113
[14] Huang, T.; Li, C.: Chaotic synchronization by the intermittent feedback method, J comput appl math 234, 1097-1104 (2010) · Zbl 1195.65212 · doi:10.1016/j.cam.2009.05.020
[15] Huang, T.; Li, C.; Liu, X.: Synchronization of chaotic systems with delay using intermittent linear state feedback, Chaos 18, 033122 (2008) · Zbl 1309.34096
[16] Huang, T.; Li, C.; Yu, W.; Chen, G.: Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback, Nonlinearity 22, 569-584 (2009) · Zbl 1167.34386 · doi:10.1088/0951-7715/22/3/004
[17] Kurt, E.: Nonlinearities from a non-autonomous chaotic circuit with a non-autonomous model of chuas diode, Phys scr 74, 22-27 (2006)
[18] Laub, A. J.: Schur techniques for solving Riccati differential equations, Lecture notes in control information sciences, 165-174 (1982) · Zbl 0492.93039
[19] Lei, Y.; Xu, W.; Xu, Y.; Fang, T.: Chaos control by harmonic excitation with proper random phase, Chaos solitons fract 21, 1175-1181 (2004) · Zbl 1129.37321 · doi:10.1016/j.chaos.2003.12.086
[20] Li, G. H.; Zhou, S. P.; Yang, K.: Generalized projective synchronization between two different chaotic systems using active backstepping control, Phys lett A 355, 326-330 (2006)
[21] Liu, X.: Impulsive synchronization of chaotic system subject to time delay, Nonlinear anal 71, 1320-1327 (2009)
[22] Lu, J.; Cao, J.: Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters, Chaos 15, 043901 (2005) · Zbl 1144.37378 · doi:10.1063/1.2089207
[23] Lu, J.; Ho, D. W. C.; Cao, J.; Kurths, J.: Exponential synchronization of linearly coupled neural networks with impulsive disturbances, IEEE trans neural netw 22, 329-335 (2011)
[24] Niamsup, P.; Mukdasai, K.; Phat, V. N.: Improved exponential stability for time-varying systems with nonlinear delayed perturbations, Appl math comput 204, 490-495 (2008) · Zbl 1168.34355 · doi:10.1016/j.amc.2008.07.022
[25] Phat, V. N.; Ha, Q. P.: H$\infty $ control and exponential stability of nonlinear non-autonomous systems with time-varying delay, J optim theory appl 142, 603-618 (2009) · Zbl 1178.93047 · doi:10.1007/s10957-009-9512-9
[26] Phat, V. N.; Niamsup, P.: Stability of linear time-varying delay systems and applications to control problems, J comput appl math 194, 343-356 (2006) · Zbl 1161.34353 · doi:10.1016/j.cam.2005.07.021
[27] Sun, J.: Global synchronization criteria with channel time-delay for chaotic time-delay systems, Chaos solitons fract 21, 967-975 (2004) · Zbl 1045.34050 · doi:10.1016/j.chaos.2003.12.055
[28] Suykens, J. A. K.; Vandewalle, J.; Chua, Q. L.: Nonlinear H$\infty $ synchronization of chaotic Lur’e systems, Internat J bifur chaos appl sci eng 7, 1323-1335 (1997) · Zbl 0967.93508 · doi:10.1142/S0218127497001059
[29] William, T.: Riccati differential equations, (1972) · Zbl 0254.34003
[30] Xia, W.; Cao, J.: Adaptive synchronization of a switching system and its applications to secure communications, Chaos 18, 023128 (2008) · Zbl 1307.34085
[31] Xia, W.; Cao, J.: Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos 19, 013120 (2009) · Zbl 1311.93061
[32] Zochowski, M.: Intermittent dynamical control, Phys D 145, 181-190 (2000) · Zbl 0963.34030 · doi:10.1016/S0167-2789(00)00112-3