Kybernetika 56 no. 4, 753-766, 2020

Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems

Song ZhengDOI: 10.14736/kyb-2020-4-0753

Abstract:

This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems, where the constrained time delay are considered in the conditions obtained. To protrude the availability of the devised stability scheme, simulation examples are ultimately demonstrated.

Keywords:

stability, uncertain, complex-variable system, delayed, aperiodically intermittent control

Classification:

34D06, 34D35, 34C15

References:

  1. S. Cai, P. Zhou and Z. Liu: Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control. Chaos 24 (2014), 033102.   DOI:10.1063/1.4886186
  2. T. W. Carr and I. B. Schwartz: Controlling the unstable steady state in a multimode laser. Phys. Rev. E 51 (1995), 5109-5111.   DOI:10.1103/physreve.51.5109
  3. T. Chen, X. Liu and W. Lu: Pinning complex networks by a single controller. IEEE Trans. Circuits Systems I 54 (2007), 1317-1326.   DOI:10.1109/tcsi.2007.895383
  4. Y. Dong, S. Liang, L. Guo and W. Wang: Exponential stability and stabilization for uncertain discrete-time periodic systems with time-varying delay. IMA J. Math. Control Inform. 35 (2018), 3, 963-986.   DOI:10.1093/imamci/dnx003
  5. T. Fang and J. Sun: Stability of complex-valued impulsive system with delay. Appl. Math. Comput. 240 (2014), 102-108.   DOI:10.1016/j.amc.2014.04.062
  6. T. Fang and J. Sun: Stability of complex-valued impulsive and switching system and application to the Lü system. Nonlinear Analysis: Hybrid Systems 14 (2015), 38-46.   DOI:10.1016/j.nahs.2014.04.004
  7. A. C. Fowler, J. D. Gibbon and M. J. McGuinness: The complex Lorenz equations. Physica D 4 (1982), 139-163.   DOI:10.1016/0167-2789(82)90057-4
  8. T. Huang, C. Li and X. Liu: Synchronization of chaotic systems with delay using intermittent linear state feedback. Chaos 18 (2008), 033122.   DOI:10.1063/1.2967848
  9. C. Jiang, F. Zhang and T. Li: Synchronization and antisynchronization of N-coupled fractional-order complex chaotic systems with ring connection. Math. Methods Appl. Sci. 41 (2018), 2625-2638.   DOI:10.1002/mma.4765
  10. C. D. Li, X. F. Liao and T. W. Huang: Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17 (2007), 013103.   DOI:10.1063/1.2430394
  11. N. Li, H. Sun and Q. Zhang: Exponential synchronization of united complex dynamical networks with multi-links via adaptive periodically intermittent control. IET Control Theory Appl. 159 (2013), 1725-1736.   DOI:10.1049/iet-cta.2013.0159
  12. Y. Liang and X. Wang: Synchronization in complex networks with non-delay and delay couplings via intermittent control with two switched periods. Physica A 395 (2014), 434-444.   DOI:10.1016/j.physa.2013.10.002
  13. X. Liu and T. Chen: Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans. Automat. Control 60 (2015), 3316-3321.   DOI:10.1109/tac.2015.2416912
  14. X. Liu, Y. Liu and L. Zhou: Quasi-synchronization of nonlinear coupled chaotic systems via aperiodically intermittent pinning control. Neurocomputing 173 (2016), 759-767.   DOI:10.1016/j.neucom.2015.08.027
  15. L. Liu, Z. Wang, Z. Huang and H. Zhang: Adaptive predefined performance control for IMO systems with unknown direction via generalized fuzzy hyperbolic model. IEEE Trans. Fuzzy Systems 25 (2007), 527-542.   DOI:10.1109/tfuzz.2016.2566803
  16. G. M. Mahmoud, T. Bountis and E. E. Mahmoud: Active control and global synchronization for complex Chen and Lü systems. Int. J. Bifurcat. Chaos 17 (2014), 4295-4308.   DOI:10.1142/s0218127407019962
  17. G. Mahmoud, E. Mahmoud and A. Arafa: On modified time delay hyperchaotic complex Lü system. Nonlinear Dynamics 80 (2015), 855-869.   DOI:10.1007/s11071-015-1912-9
  18. G. Mahmoud, E. Mahmoud and A. Arafa: Projective synchronization for coupled partially linear complex-variable systems with known parameters. Math. Methods Appl. Sci. 40 (2017), 1214-1222.   DOI:10.1002/mma.4045
  19. C. Z. Ning and H. Haken: Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. Phys. Rev. A 41 (1990), 3826-3837.   DOI:10.1103/physreva.41.3826
  20. E. Ott, C. Grebogi and J. Yorke: Controlling chaos. Phys. Rev. Lett. 64 (1990), 1196.   DOI:10.1103/physrevlett.64.1196
  21. L. M. Pecora and T. L. Carroll: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821-824.   DOI:10.1103/physrevlett.64.821
  22. J. Qiu, L. Cheng, X, Chen, J. Lu and H. He: Semi-periodically intermittent control for synchronization of switched complex networks: a mode-dependent average dwell time approach. Nonlinear Dynamics 83 (2016), 1757-1771.   DOI:10.1007/s11071-015-2445-y
  23. J. Starrett: Control of chaos by occasional bang-bang. Phys. Rev. E 67 (2003), 036203.   DOI:10.1103/physreve.67.036203
  24. W. Xia and J. Cao: Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19 (2009), 013120.   DOI:10.1063/1.3071933
  25. S. Zheng: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems. Nonlinear Dynamics 74 (2013), 957-967.   DOI:10.1007/s11071-013-1015-4
  26. S. Zheng: Impulsive complex projective synchronization in drive-response complex coupled dynamical networks. Nonlinear Dynamics 79 (2015), 147-161.   DOI:10.1007/s11071-014-1652-2
  27. S. Zheng: Stability of uncertain impulsive complex-variable chaotic systems with time- varying delays. ISA Trans. 58 (2015), 20-26.   DOI:10.1016/j.isatra.2015.05.016
  28. S. Zheng: Further Results on the impulsive synchronization of uncertain complex-variable chaotic delayed systems. Complexity 21 (2016), 131-142.   DOI:10.1002/cplx.21641
  29. S. Zheng: Synchronization analysis of time delay complex-variable chaotic systems with discontinuous coupling. J. Franklin Inst. 353 (2016), 1460-1477.   DOI:10.1016/j.jfranklin.2016.02.006
  30. S. Zheng: Stability analysis of uncertain complex-variable delayed nonlinear systems via intermittent control with multiple switched periods. Kybernetika 54 (2018), 937-957.   DOI:10.14736/kyb-2018-5-0937
  31. S. Zheng, Q. Bi and G. Cai: Adaptive projective synchronization in complex networks with time-varying coupling delay. Phys. Lett. A 373 (2009), 1553-1559.   DOI:10.1016/j.physleta.2009.03.001
  32. M. Zochowski: Intermittent dynamical control. Physica D 145 (2000), 181-190.   DOI:10.1016/s0167-2789(00)00112-3