Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays

Abstract

This paper reports the boundedness and stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) with multiple delays. Without imposing linear growth condition, the boundedness and exponential stability of the exact solution are investigated by Lyapunov functional method. In particular, using the M-matrix technique, the mean square exponential stability is obtained. Finally, three examples are presented to verify our results.

This is a preview of subscription content, access via your institution.

References

  1. 1

    Song J, Niu Y, Zou Y Y. Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities. Automatica, 2018, 93: 33–41

    MathSciNet  Article  MATH  Google Scholar 

  2. 2

    Fei WY, Hu L J, Mao X R, et al. Generalized criteria on delay dependent stability of highly nonlinear hybrid stochastic systems. Int J Robust Nonlinear Control, 2019, 29: 1201–1215

    MathSciNet  Article  MATH  Google Scholar 

  3. 3

    Wang B, Zhu Q. Stability analysis of semi-Markov switched stochastic systems. Automatica, 2018, 94: 72–80

    MathSciNet  Article  MATH  Google Scholar 

  4. 4

    Fei C, Shen M X, Fei W Y, et al. Stability of highly nonlinear hybrid stochastic integro-differential delay equations. Nonlinear Anal-Hybrid Syst, 2019, 31: 180–199

    MathSciNet  Article  MATH  Google Scholar 

  5. 5

    Mao X R, Yuan C G. Stochastic Differential Equations with Markovian Switching. London: Imperial College Press, 2006

    Google Scholar 

  6. 6

    Song G F, Lu Z Y, Zheng B C, et al. Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state. Sci China Inf Sci, 2018, 61: 070213

    MathSciNet  Article  Google Scholar 

  7. 7

    Yan Z G, Song Y X, Park J H. Finite-time stability and stabilization for stochastic markov jump systems with modedependent time delays. ISA Trans, 2017, 68: 141–149

    Article  Google Scholar 

  8. 8

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

    Google Scholar 

  9. 9

    Cao Y Y, Lam J, Hu L. Delay-dependent stochastic stability and H1 analysis for time-delay systems with Markovian jumping parameters. J Franklin Inst, 2003, 340: 423–434

    MathSciNet  Article  MATH  Google Scholar 

  10. 10

    Wu Y, Liu M, Wu X, et al. Input-to-state stability analysis for stochastic delayed systems with markovian switching. IEEE Access, 2017, 5: 23663–23671

    Article  Google Scholar 

  11. 11

    Wu X T, Tang Y, Zhang W B. Stability analysis of stochastic delayed systems with an application to multi-agent systems. IEEE Trans Autom Control, 2016, 61: 4143–4149

    Article  Google Scholar 

  12. 12

    Hu L J, Mao X R, Shen Y. Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Syst Control Lett, 2013, 62: 178–187

    MathSciNet  Article  MATH  Google Scholar 

  13. 13

    Hu L J, Mao X R, Zhang L G. Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations. IEEE Trans Autom Control, 2013, 58: 2319–2332

    MathSciNet  Article  MATH  Google Scholar 

  14. 14

    Fei W Y, Hu L J, Mao X R, et al. Delay dependent stability of highly nonlinear hybrid stochastic systems. Automatica, 2017, 82: 165–170

    MathSciNet  Article  MATH  Google Scholar 

  15. 15

    Fei W Y, Hu L J, Mao X R, et al. Structured robust stability and boundedness of nonlinear hybrid delay systems. SIAM J Control Optim, 2018, 56: 2662–2689

    MathSciNet  Article  MATH  Google Scholar 

  16. 16

    Obradović M, Milošević M. Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler-Maruyama method. J Comput Appl Math, 2017, 309: 244–266

    MathSciNet  Article  MATH  Google Scholar 

  17. 17

    Chen H B, Shi P, Lim C L, et al. Exponential stability for neutral stochastic Markov systems with time-varying delay and its applications. IEEE Trans Cybern, 2016, 46: 1350–1362

    Article  Google Scholar 

  18. 18

    Mao W H, Deng F Q, Wan A H. Robust H 2/H global linearization filter design for nonlinear stochastic time-varying delay systems. Sci China Inf Sci, 2016, 59: 032204

    Article  Google Scholar 

  19. 19

    Mo H Y, Li M L, Deng F Q, et al. Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps. Sci China Inf Sci, 2018, 61: 070214

    MathSciNet  Article  Google Scholar 

  20. 20

    Deng F Q, Mao W H, Wan A H. A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems. Appl Math Comput, 2013, 221: 132–143

    MathSciNet  MATH  Google Scholar 

  21. 21

    Shen M X, Fei W Y, Mao X R, et al. Exponential stability of highly nonlinear neutral pantograph stochastic differential equations. Asian J Control, 2018. doi: https://doi.org/10.1002/asjc.1903

    Google Scholar 

  22. 22

    Wu F K, Hu S G, Huang CM. Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay. Syst Control Lett, 2010, 59: 195–202

    MathSciNet  Article  MATH  Google Scholar 

  23. 23

    Shen M X, Fei W Y, Mao X R, et al. Stability of highly nonlinear neutral stochastic differential delay equations. Syst Control Lett, 2018, 115: 1–8

    MathSciNet  Article  MATH  Google Scholar 

  24. 24

    Luo Q, Mao X R, Shen Y. New criteria on exponential stability of neutral stochastic differential delay equations. Syst Control Lett, 2006, 55: 826–834

    MathSciNet  Article  MATH  Google Scholar 

  25. 25

    Song Y, Shen Y. New criteria on asymptotic behavior of neutral stochastic functional differential equations. Automatica, 2013, 49: 626–632

    MathSciNet  Article  MATH  Google Scholar 

  26. 26

    Kolmanovskii V, Koroleva N, Maizenberg T, et al. Neutral stochastic differential delay equations with Markovian switching. Stoch Anal Appl, 2003, 21: 819–847

    MathSciNet  Article  MATH  Google Scholar 

  27. 27

    Mao X R, Shen Y, Yuan C G. Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching. Stoch Proc Appl, 2008, 118: 1385–1406

    MathSciNet  Article  MATH  Google Scholar 

  28. 28

    Li M L, Deng F Q. Almost sure stability with general decay rate of neutral stochastic delayed hybrid systems with Lévy noise. Nonlinear Anal-Hybrid Syst, 2017, 24: 171–185

    MathSciNet  Article  MATH  Google Scholar 

  29. 29

    Zhao N, Zhang X, Xue Y, et al. Necessary conditions for exponential stability of linear neutral type systems with multiple time delays. J Franklin Inst, 2018, 355: 458–473

    MathSciNet  Article  MATH  Google Scholar 

  30. 30

    Wang J J, Hu P, Chen H B. Delay-dependent exponential stability for neutral stochastic system with multiple timevarying delays. IET Control Theory Appl, 2014, 8: 2092–2101

    MathSciNet  Article  Google Scholar 

  31. 31

    Park J H. A new delay-dependent criterion for neutral systems with multiple delays. J Comput Appl Math, 2001, 136: 177–184

    MathSciNet  Article  MATH  Google Scholar 

  32. 32

    Zhang H G, Dong M, Wang Y C, et al. Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping. Neurocomputing, 2010, 73: 2689–2695

    Article  Google Scholar 

  33. 33

    Lu S, Ge W. Existence of positive periodic solutions for neutral logarithmic population model with multiple delays. J Comput Appl Math, 2004, 166: 371–383

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 71571001, 71873002), Natural Science Foundation of Universities of Anhui Province (Grant No. KJ2018A0119), and Promoting Plan of Higher Education of Anhui Province (Grant No. TSKJ2016B11).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Weiyin Fei.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shen, M., Fei, C., Fei, W. et al. Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays. Sci. China Inf. Sci. 62, 202205 (2019). https://doi.org/10.1007/s11432-018-9755-7

Download citation

Keywords

  • hybrid delay systems
  • neutral stochastic systems
  • multiple delays
  • highly nonlinear