Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control

International Journal of Control

Volumn 86, Issue 1, 2013, Pages 107-119

  Lee, Tae H ^a   Park, Ju H ^a   Lee, S M ^b   Kwon, O M ^c  

^a Yeungnam University   (South Korea)

^b Daegu University   (South Korea)

^c Chungbuk National University   (South Korea)

Author keywords

nonlinear chaotic systems; randomly occurring uncertainties; sampled data control; synchronisation; variable sampling

Indexed keywords

BERNOULLI; EXISTENCE CONDITIONS; HYPERCHAOTIC; INPUT DELAYS; LYAPUNOV FUNCTIONALS; LYAPUNOV STABILITY THEORY; MEAN-SQUARE; NONLINEAR CHAOTIC SYSTEMS; NORM-BOUNDED UNCERTAINTY; NUMERICAL EXAMPLE; RANDOMLY OCCURRING UNCERTAINTIES; SAMPLED-DATA CONTROL; SAMPLED-DATA CONTROLLER; SAMPLING INTERVAL; SAW-TOOTH STRUCTURE; VARIABLE SAMPLING; WHITE NOISE SEQUENCE;

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; SYNCHRONIZATION; WHITE NOISE;

CHAOTIC SYSTEMS;

EID: 84871428495     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207179.2012.720034     Document Type: Article

References (48)

1. Astrom, K., and Wittenmark, B. (1989), Adaptive Control, Reading, MA: Addison-Wesley.\
2. Balasubramaniam, P., Chandran, R., and Theesar, S.J.S. (2011), 'Synchronization of Chaotic Nonlinear Continuous Neural Networks with Time-varying Delay', Cognitive Neurodynamics, 5, 361-371.
3. Balasubramaniam, P., Lakshmanan, S., and Theesar, S.J.S. (2010), 'State Estimation for Markovian Jumping Recurrent Neural Networks with Interval Time-varying Delays', Nonlinear Dynamics, 60, 661-675.
4. Balasubramaniam, P., Vembarasan, V., and Rakkiyappan, R. (2011), 'Delay-dependent Robust Exponential State Estimation of Markovian Jumping Fuzzy Hopfield Neural Networks with Mixed Random Time-varying Delays', Communications in Nonlinear Science and Numerical Simulation, 16, 2109-2129.
5. Balasubramaniam, P., Vembarasan, V., and Rakkiyappan, R. (2012), 'Delay-dependent Robust Asymptotic State Estimation of TakagiYSugeno Fuzzy Hopfield Neural Networks with Mixed Interval Time-varying Delays', Expert Systems with Applications, 39, 472-481.
6. Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V. (1994), Linear Matrix Inequalities in Systems and Control Theory, Philadelphia, PA: SIAM.
7. Cao, J., Ho, D.W.C., and Yang, Y. (2009), 'Projective Synchronization of a Class of Delayed Chaotic Systems via Impulsive Control', Physics Letters A, 373, 3128-3133.
8. Cao, J., Li, H.X., and Ho, D.W.C. (2005), 'Synchronization Criteria of Lur'e Systems with Time-delay Feedback Control', Chaos, Solitons and Fractals, 23, 1285-1298.
9. Celikovsky, S., and Chen, G. (2005), 'Secure Synchronization of a Class of Chaotic Systems from a Nonlinear Observer Approach', IEEE Transactions on Automatic Control, 50, 76-82. (Pubitemid 40173725)
10. Chua, L.O., Komuro, M., and Matsumoto, T. (2000), 'The Double Scroll Family', IEEE Transactions on Cirtuis and Systems I, 33, 1072-1118.
11. Ding, D., Wang, Z., Shen, B., and Shu, H. (2012), 'State Estimation for Discrete-time Complex Networks with Randomly Occurring Sensor Saturations and Randomly Varying Sensor Delays', IEEE Transactions on Neural Networks and Learning Systems, 23, 725-736.
12. Faydasicok, O., and Arik, S. (2012), 'Equilibrium and Stability Analysis of Delayed Neural Networks under Parameter Uncertainties', Applied Mathematics and Computation, 218, 6716-6726.
13. Gao, H., Meng., X, and Chen, T. (2008), 'Stabilization of Networked Control Systems with New Delay Characterization', IEEE Transactions on Automatic Control, 53, 2142-2148.
14. Gao, H., Wu, J., and Shi, P. (2009), 'Robust Sampled-data H1 Control with Stochastic Sampling', Automatica, 45, 1729-1736.
15. Gu, K., Kharitonov, V.K., and Chen, J. (2003), Stability of Time-delay Systems, Boston: Birkhauser.
16. He, W., Qian, F., Cao, J., and Han, Q.L. (2011), 'Impulsive Synchronization of Two Nonidentical Chaotic Systems with Time-varying Delay', Physics Letters A, 375, 498-504.
17. Hu, B., and Michel, A.N. (2000), 'Stability Analysis of Digital Feedback Control Systems with Time-varying Sampling Periods', Automatica, 36, 897-905. (Pubitemid 30587674)
18. Hu, C., Yu, J., Jiang, H., and Teng, Z. (2012a), 'Exponential Synchronization for ReactionYDiffusion Networks with Mixed Delays in Terms of P-norm via Intermittent Driving', Neural Networks, 31, 1-11.
19. Hu, J., Wang, Z., Gao, H., and Stergioulas, L.K. (2012b), 'Robust Sliding Mode Control for Discrete Stochastic Systems with Mixed Time-delays, Randomly Occurring Uncertainties and Nonlinearities', IEEE Transactions on Industrial Electronics, 59, 3008-3015.
20. Hu, S., Yue, D., and Liu, J. (2012c), 'H1 Filtering for Networked Systems with Partly Known Distribution Transmission Delays', Information Sciences, 194, 270-282.
21. Lam, H.K., Ling, W.K., Lu, H.H.C., and Ling, S.S.H. (2008), 'Synchronization of Chaotic Systems using Timedelayed Fuzzy State-feedback Controller', IEEE Transactions on Circuits and Systems I, 55, 893-903. (Pubitemid 351751808)
22. Li, N., Zhang, Y., Hu, J., and Nie, Z. (2011), 'Synchronization for General Complex Dynamical Networks with Sampled-data', Neurocomputing, 74, 805-811.
23. Li, Y., Zhang, Q., and Jing, C. (2009), 'Stochastic Stability of Networked Control Systems with Time-varying Sampling Periods', International Journal of Information and Systems Sciences, 5, 494-502.
24. Li, Z., Duan, Z., Xie, L., and Liu, X. (2012), 'Distributed Robust Control of Linear Multi-agent Systems with Parameter Uncertainties', International Journal of Control, 19, 1-12.
25. Lin, T.C., and Kuo, C.H. (2011), 'H1 Synchronization of Uncertain Fractional Order Chaotic Systems: Adaptive Fuzzy Approach', ISA Transactions, 50, 548-556.
26. Liu, K., and Fridman, E. (2012), 'Wirtinger's Inequality and Lyapunov-based Sampled-data Stabilisation', Automatica, 48, 102-108.
27. Liu, K., Suplin, V., and Fridman, E. (2011), 'Stability of Linear Systems with General Sawtooth Delay', IMA Journal of Mathematical Control and Information, 27, 419-436.
28. Lu, J.G., and Hill, D.J. (2008), 'Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach', IEEE Transactions on Circuits and Systems II, 55, 586-590.
29. Mikheev, Y., Sobolev, V., and Fridman, E. (1988), 'Asymptotic Analysis of Digital Control Systems', Automation and Remote Control, 49, 1175-1180.
30. Mohammad-Hoseini, S., Farrokhi, M., and Koshkouei, A.J. (2008), 'Robust Adaptive Control of Uncertain Non-linear Systems using Neural Networks', International Journal of Control, 81, 1319-1330.
31. Naghshtabrizi, P., and Hespanha, J.P. (2005), 'Designing an Observer-based Controller for a Network Control System', in 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, 12-15 December 2005, pp. 848-853. (Pubitemid 46297073)
32. Ozdemir, N., and Townley, T. (2003), 'Integral Control by Variable Sampling Based on Steady-state Data', Automatica, 39, 135-140. (Pubitemid 35412303)
33. Park, J.H. (2006), 'Synchronization of Genesio Chaotic System via Backstepping Approach', Chaos, Solitons and Fractals, 27, 1369-1375. (Pubitemid 41329830)
34. Park, P.G., Ko, J.W., and Jeong, C. (2011), 'Reciprocally Convex Approach to Stability of Systems with Timevarying Delays', Automatica, 7, 235-238.
35. Pecora, L.M., and Carroll, T.L. (1990), 'Synchronization in Chaotic Systems', Physics Review Letters, 64, 821-825.
36. Peng, C., Han, Q.L., Yue, D., and Tian, E. (2011), 'Sampleddata Robust H1 Control for T-S Fuzzy Systems with Time Delay and Uncertainties', Fuzzy Sets and Systems, 179, 20-33.
37. Peng, C., Yue, D., Tian, E., and Gu, Z. (2009), 'A Delay Distribution Based Stability Analysis and Synthesis Approach for Networked Control Systems', Journal of the Franklin Institute, 346, 349-365.
38. Rössler, O.E. (1979), 'An Equation for Hyperchaos', Physics Letters A, 71, 155-157.
39. Sala, A. (2005), 'Computer Control Under Time-varying Sampling Period: An LMI Gridding Approach', Automatica, 41, 2077-2082. (Pubitemid 41525665)
40. Tahara, S., Fujii, T., and Yokoyama, T. (2007), 'Variable Sampling Quasi-multirate Deadbeat Control Method for Single-phase PWM Inverter in Low-carrier Frequency', in Proceedings of power conversion conference, pp. 804-809. (Pubitemid 47468601)
41. Tian, E., Yue, D., and Peng, C. (2010), 'Reliable Control for Networked Control Systems with Probabilistic Actuator Fault and Random Delays', Journal of the Franklin Institute, 347, 1907-1926.
42. Xiao, M., and Cao, J. (2009), 'Synchronization of a Chaotic Electronic Circuit System with Cubic Term via Adaptive Feedback Control', Communications in Nonlinear Science and Numerical Simulation, 14, 3379-3388.
43. Yang, G.H., and Ye, D. (2009), 'Adaptive Robust H1 Filter Design for Linear Systems with Time-varying Uncertainty', International Journal of Control, 82, 517-524.
44. Yau, H.T. (2008), 'Chaos Synchronization of Two Uncertain Chaotic Nonlinear Gyros using Fuzzy Sliding Mode Control', Mechanical Systems and Signal Processing, 22, 408-418.
45. Yue, D., Han, Q.L., and Peng, C. (2004), 'State Feedback Controller Design of Networked Control Systems', IEEE Transactions on Circuits and Systems II, 51, 640-644.
46. Yue, D., Tian, E., Wang, Z., and Lam, J. (2009), 'Stabilization of Systems with Probabilistic Interval Input Delays and its Applications to Networked Control Systems', IEEE Transactions on Systems, Man, and Cybernetics A: Systems and Humans, 39, 939-945.
47. Zhang, C.K., He, Y., and Wu, M. (2010), 'Exponential Synchronization of Neural Networks with Time-varying Mixed Delays and Sampled-data', Neurocomputing, 74, 265-273.
48. Zheng, C.D., Zhou, F., and Wang, Z. (2012), 'Stochastic Exponential Synchronization of Jumping Chaotic Neural Networks with Mixed Delays', Communications in Nonlinear Science and Numerical Simulation, 17, 1273-1291.