Abstract
This paper investigates the networked reliable synchronization problem of chaotic Lur’e systems containing the sector- and slope-restricted nonlinearities. The reliable synchronization of chaotic Lur’e systems is achieved based on networked control techniques. Moreover, some sufficient conditions are obtained and these conditions depend on various network-related parameters, fault indicating matrices, sector and slope bounds. Finally, a numerical example is provided to illustrate the validity of the proposed method.
Similar content being viewed by others
References
S. Boyd, L.E. Ghauoi, E. Feron, V. Balakrishan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)
J.D. Cao, H.X. Li, D.W.C. Ho, Synchronization criteria of Lur’e systems with time-delay feedback control. Chaos Soliton. Fract. 23(4), 1285–1298 (2005)
A. Chandrasekar, R. Rakkiyappan, J.D. Cao, S. Lakshmanan, Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Neural Netw. 57, 79–93 (2014)
W.H. Chen, Z. Wang, X. Lu, On sampled-data control for master-slave synchronization of chaotic Lur’e systems. IEEE Trans. Circ. Syst. II Exp. Briefs 59(8), 515–519 (2012)
L.E. Ghaoui, F. Oustry, M. AitRami, A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control 42(8), 1171–1176 (1997)
K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems (Birkhäuser, Boston, 2003)
H.M. Guo, S.M. Zhong, F.Y. Gao, Design of PD controller for master-slave synchronization of Lur’e systems with time-delay. Appl. Math. Comput. 212(1), 86–93 (2009)
Q.-L. Han, On designing time-varying delay feedback controllers for master-slave synchronization of Lur’e systems. IEEE Trans. Circ. Syst. I Regul. Pap 54(7), 1573–1583 (2007)
X.F. Jiang, Q.-L. Han, S.R. Liu, A.K. Xue, A new \(\text{ H }_{\infty }\) stabilization criterion for networked control systems. IEEE Trans. Autom. Control 53(4), 1025–1032 (2008)
J.G. Lu, D.J. Hill, Impulsive synchronization of chaotic Lur’e systems by linear static measurement feedback: an LMI approach. IEEE Trans. Circ. Syst. II Exp. Briefs 54(8), 710–714 (2007)
J.G. Lu, D.J. Hill, Global asymptotical synchronization of chaotic Lur’e systems using sampled data: a linear matrix inequality approach. IEEE Trans. Circ. Syst. II Exp. Briefs 55(6), 586–590 (2008)
J.Q. Lu, J.D. Cao, D.W.C. Ho, Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay. IEEE Trans. Circ. Syst. I Regul. Pap. 55(5), 1347–1356 (2008)
D.Z. Ma, H.G. Zhang, Z.S. Wang, J. Feng, Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller. Chin. Phys. B 19(5), 050506 (2010)
T.D. Ma, H.G. Zhang, J. Fu, Exponential synchronization of stochastic impulsive perturbed chaotic Lur’e systems with time-varying delay and parametric uncertainty. Chin. Phys. B 17(2), 4407–4417 (2008)
R. Rakkiyappan, A. Chandrasekar, J.H. Park, O.M. Kwon, Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control. Nonlinear Anal. Hybrid 14, 16–37 (2014)
R. Rakkiyappan, R. Sivasamy, S. Lakshmanan, Exponential synchronization of chaotic Lur’e systems with time-varying delay via sampled-data control. Chin. Phys. B 23(6), 060504 (2014)
R. Rakkiyappan, R. Sivasamy, X. Li, Synchronization of identical and nonidentical memristor-based chaotic systems via active backstepping control technique. Circ. Syst. Signal Process. 34(3), 763–778 (2015)
R. Sivasamy, R. Rakkiyappan, Improved stability criteria for neutral type Lur’e systems with time-varying delays. Appl. Math. Lett. 38, 168–173 (2014)
S.J.S. Theesar, P. Balasubramaniam, Secure communication via synchronization of Lur’e systems using sampled-data controller. Circ. Syst. Signal Process. 33(1), 37–52 (2014)
Y.Q. Wu, H.Y. Su, Z.G. Wu, Asymptotical synchronization of chaotic Lur’e systems under time-varying sampling. Circ. Syst. Signal Process. 33(3), 699–712 (2014)
Y.Q. Wu, H.Y. Su, Z.G. Wu, \(\text{ H }_\infty \) filtering for discrete fuzzy stochastic systems with randomly occurred sensor nonlinearities. Signal Process. 108, 288–296 (2015)
Y.Q. Wu, H.Y. Su, Z.G. Wu, Synchronisation control of dynamical networks subject to variable sampling and actuators saturation. IET Control Theory Appl. 9(3), 381–391 (2015)
Y.Q. Wu, Z.G. Wu, H.Y. Su, Robust output synchronization of non-identical linear agents via internal model principle. IET Control Theory Appl. (2014). doi:10.1049/iet-cta.2014.1192
Z.G. Wu, P. Shi, H.Y. Su, J. Chu, Sampled-data synchronization of chaotic Lur’e systems with time delays. IEEE Trans. Neural Netw. Learn. Syst. 24(3), 410–421 (2013)
X.Q. Xiao, L. Zhou, Z.J. Zhang, Synchronization of chaotic Lur’e systems with quantized sampled-data controller. Commun. Nonlinear Sci. Numer. Simul. 19(6), 2039–2047 (2014)
D. Yang, Robust networked \(\text{ H }_{\infty }\) synchronization of nonidentical chaotic Lur’e systems. Chin. Phys. B 23(1), 010504 (2014)
D. Yang, K.-Y. Cai, Decentralized networked stabilization for interconnected nonlinear systems: a fuzzy control approach. In: Proceedings of the 8th world congress on intelligent control and automation (WCICA), 4823–4828, Jinan, China, (2010)
C. Yin, S.M. Zhong, W.F. Chen, Design PD controller for master-slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities. Commun. Nonlinear Sci. Numer. Simul. 16(3), 1632–1639 (2011)
C.K. Zhang, Y. He, M. Wu, Improved global asymptotical synchronization of chaotic Lur’e systems with sampled-data control. IEEE Trans. Circ. Syst. II Exp. Briefs 56(4), 320–324 (2009)
C.K. Zhang, L. Jiang, Y. He et al., Asymptotical synchronization for chaotic Lur’e systems using sampled-data control. Commun. Nonlinear Sci. Numer. Simul. 18(10), 2743–2751 (2013)
Acknowledgments
This work was supported by the Natural Science Foundation of China under Grants 61203076, the Natural Science Foundation of Tianjin City under Grant 13JCQNJC03500, and the Natural Science Foundation of Hebei Province under Grant F2012202100.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, D. Networked Reliable Synchronization of Chaotic Lur’e Systems with Sector- and Slope-Restricted Nonlinearities. Circuits Syst Signal Process 35, 1665–1675 (2016). https://doi.org/10.1007/s00034-015-0135-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-015-0135-0