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Stabilization for multi-group coupled stochastic models by delay feedback control and nonlinear impulsive control

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Abstract

Stabilization for multi-group coupled models stochastic by delay feedback control and nonlinear impulsive control are considered in this paper. Using graph theory and Lyapunov method, some sufficient conditions are acquired by some control methods. Those criteria are easier to verify and no need to solve any linear matrix inequalities. These results can be designed more easily in practice. At last, the effectiveness and advantage of the theoretical results are verified by an example.

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References

  1. Harary F. Graph Theory. Boston: Addison-Wesley, 1969

    Book  MATH  Google Scholar 

  2. West D B. Introduction to Graph Theory. Upper Saddle River: Prentice Hall, 1996

    MATH  Google Scholar 

  3. Guo H B, Li M Y, Shuai Z S. A graph-theoretic approach to the method of global Lyapunov functions. Proc Amer Math Soc, 2008, 136: 2793–2802

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang C M, Li W X, Wang K. Graph-theoretic approach to stability of multi-group models with dispersal. Discrete Contin Dyn Syst-Ser B, 2015, 20: 259–280

    Article  MathSciNet  MATH  Google Scholar 

  5. Fotsin H B, Daafouz J. Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification. Phys Lett A, 2005, 339: 304–315

    Article  MATH  Google Scholar 

  6. Huang D. Simple adaptive-feedback controller for identical chaos synchronization. Phys Rev E, 2005, 71: 037203

    Article  Google Scholar 

  7. Lu J Q, Cao J D. Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos, 2005, 15: 043901

    Article  MathSciNet  MATH  Google Scholar 

  8. Park J H. Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. J Comput Appl Math, 2008, 213: 288–293

    Article  MATH  Google Scholar 

  9. Agiza H N, Yassen M T. Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys Lett A, 2001, 278: 191–197

    Article  MathSciNet  MATH  Google Scholar 

  10. Lei Y M, Xu W, Zheng H C. Synchronization of two chaotic nonlinear gyros using active control. Phys Lett A, 2005, 343: 153–158

    Article  MATH  Google Scholar 

  11. Wang C C, Su J P. A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos Soliton Fract, 2004, 20: 967–977

    Article  MathSciNet  MATH  Google Scholar 

  12. Park J H. Synchronization of Genesio chaotic system via backstepping approach. Chaos Soliton Fract, 2006, 27: 1369–1375

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen W M, Xu S Y, Zou Y. Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control. Syst Control Lett, 2016, 88: 1–13

    Article  MathSciNet  MATH  Google Scholar 

  14. Mao X R, Lam J, Huang L R. Stabilisation of hybrid stochastic differential equations by delay feedback control. Syst Control Lett, 2008, 57: 927–935

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhu Q X, Zhang Q Y. pth moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay. IET Control Theory Appl, 2017, 11: 1992–2003

    Article  MathSciNet  Google Scholar 

  16. Fotsin H B, Woafo P. Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification. Chaos Soliton Fract, 2005, 24: 1363–1371

    Article  MathSciNet  MATH  Google Scholar 

  17. Heagy J F, Carroll T L, Pecora L M. Experimental and numerical evidence for riddled basins in coupled chaotic systems. Phys Rev Lett, 1994, 73: 3528–3531

    Article  Google Scholar 

  18. Huang L L, Feng R P, Wang M. Synchronization of chaotic systems via nonlinear control. Phys Lett A, 2004, 320: 271–275

    Article  MathSciNet  MATH  Google Scholar 

  19. Kakmeni F, Bowong S, Tchawoua C. Nonlinear adaptive synchronization of a class of chaotic systems. Phys Lett A, 2006, 355: 47–54

    Article  MATH  Google Scholar 

  20. Deng F Q, Luo Q, Mao X R. Stochastic stabilization of hybrid differential equations. Automatica, 2012, 48: 2321–2328

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhu Q X. Razumikhin-type theorem for stochastic functional differential equations with L´evy noise and Markov switching. Int J Control, 2017, 90: 1703–1712

    Article  MATH  Google Scholar 

  22. Wang B, Zhu Q X. Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems. Syst Control Lett, 2017, 105: 55–61

    Article  MathSciNet  MATH  Google Scholar 

  23. Li C D, Liao X F, Zhang X F, et al. Impulsive stabilization and synchronization of a class of chaotic delay systems. Chaos, 2005, 15: 023104

    Article  MathSciNet  MATH  Google Scholar 

  24. Peng S G, Zhang Y, Yu S M. Global mean-square exponential stabilization of stochastic system with time delay via impulsive control. Asian J Control, 2012, 14: 288–299

    Article  MathSciNet  MATH  Google Scholar 

  25. Xu L G, He D H, Ma Q. Impulsive stabilization of stochastic differential equations with time delays. Math Comput Model, 2013, 57: 997–1004

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu J, Liu X Z, Xie W C. Impulsive stabilization of stochastic functional differential equations. Appl Math Lett, 2011, 24: 264–269

    Article  MathSciNet  MATH  Google Scholar 

  27. Cheng P, Deng F Q, Peng Y J. Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay. Commun Nonlinear Sci Numer Simul, 2012, 17: 4740–4752

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhu Q. pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching. J Franklin Institute, 2014, 351: 3965–3986

    Article  MathSciNet  MATH  Google Scholar 

  29. Mao X R. Stochastic Differential Equations and Their Applications. 2nd ed. Chichester: Horwood Publishing, 2007

    MATH  Google Scholar 

  30. Yang X S, Yang Z C. Synchronization of TS fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects. Fuzzy Sets Syst, 2014, 235: 25–43

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grants Nos. 61573156, 61273126, 61503142, 11372107), Fundamental Research Funds for the Central Universities (Grant No. x2zdD2153620), Ph.D. Start-up Fund of Natural Science Foundation of Guangdong Province (Grant No. 2014A030310388), and Science and Technology Plan Foundation of Guangzhou (Grant No. 201704030131).

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Correspondence to Feiqi Deng.

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Zhang, C., Deng, F. & Luo, Y. Stabilization for multi-group coupled stochastic models by delay feedback control and nonlinear impulsive control. Sci. China Inf. Sci. 61, 70212 (2018). https://doi.org/10.1007/s11432-017-9281-3

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  • DOI: https://doi.org/10.1007/s11432-017-9281-3

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