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Non-fragile observer-based H ∞ control for neutral stochastic hybrid systems with time-varying delay

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Abstract

The non-fragile observer-based stabilization and H ∞ control problems for neutral stochastic hybrid systems with time-varying delay are studied in this paper. The time-delay is unknown and time-varying with known bounds. Based on Lyapunov functional approach combined with LMIs techniques, the delay-dependent sufficient conditions for the existence of the non-fragile observer-based H ∞ controller are given. Under the control of the non-fragile observer-based H ∞ controller, the resulting closed-loop system not only is robust stochastic exponential stable in the mean square but also satisfies the H ∞ performance level. A numerical example with simulation is given to demonstrate the feasibility and effectiveness of the proposed methods.

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References

  1. Zeng ZG, Wang J, Liao XX (2003) Global exponential stability of general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I Regul Pap 50(10):1353–1358

    Article  MathSciNet  Google Scholar 

  2. Zeng ZG, Wang J (2006) Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 17(3):623–635

    Article  MathSciNet  Google Scholar 

  3. Zeng ZG, Wang J, Liao XX (2005) Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays. IEEE Trans Circuits Syst II Express Briefs 52(1):168–173

    Article  Google Scholar 

  4. Liao XX, Wang J, Zeng ZG (2005) Global asymptotic stability and global exponential stability of delayed cellular neural networks. IEEE Trans Circuits Syst II Express Briefs 52(7):403–409

    Article  Google Scholar 

  5. Zeng ZG, Wang J, Liao XX (2004) Stability analysis of delay cellular neural networks described using cloning templates. IEEE Trans Circuits Syst I Regul Pap 50(11):1313–1324

    MathSciNet  Google Scholar 

  6. Hinrichsen D, Pritchard AJ (1998) Stochastic H ∞. SIAM J Control Optim 36(5):1504–1538

    Article  MathSciNet  Google Scholar 

  7. Bouhtouri AE, Hinrichsen D, Pritchard AJ (1999) H ∞-type control for discrete-time stochastic systems. Int J Robust Nonlinear Control 9(13):923–948

    Article  Google Scholar 

  8. Xu S, Chen T (2002) Robust H ∞ control for uncertain stochastic systems with state delay. IEEE Trans Autom Control 47(12):2089–2094

    Article  Google Scholar 

  9. Chen GC, Shen Y (2009) Robust H ∞ control for stochastic Markovian jump systems. Int J Nonlinear Sci Numer Simul 10(9):1201–1210

    Article  Google Scholar 

  10. Xu SY, Shi P, Chu YM, Zou Y (2006) Robust stochastic stability and H ∞ control of uncertain neutral stochastic time-delay systems. J Math Anal Appl 314(1):1–16

    MathSciNet  Google Scholar 

  11. Xu SY, Chen TW (2004) Output feedback control for uncertain stochastic systems with time-varying delays. Automatica 40(12):2091–2098

    MathSciNet  Google Scholar 

  12. Xu S, Chen T (2002) Reduced-order H ∞ filtering for stochastic systems. IEEE Trans Signal Process 50(12):2998–3007

    Article  MathSciNet  Google Scholar 

  13. Wei GL, Wang ZD, Shu HS (2008) Nonlinear H ∞ control for stochastic time-delay systems with Markovian switching. Chaos Solitons Fractals 35(3):442–451

    Article  MathSciNet  Google Scholar 

  14. Brayton RK (1966) Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutra type. Q Appl Math 24(3):215–224

    MathSciNet  Google Scholar 

  15. Kuang Y (1993) Delay differential equations with applications in population dynamics. Mathematics in science and engineering, 191. Academic Press, SanDiego

  16. Kolmanovskii VB, Myshkis AD (1992) Applied theory of functional differential equations. Kluwer, Dordrecht

    Google Scholar 

  17. Kolmanovskii VB, Myshkis AD (1999) Introduction to the theory and applications of functional differential equations. Kluwer, Dordrecht

    Google Scholar 

  18. Keel LH, Bhattacharyya SP (1997) Robust, fragile, or optimal? IEEE Trans Autom Control 42(8):1098–1105

    Article  MathSciNet  Google Scholar 

  19. Dorato P (1998) Non-fragile controller design, an overview. In: Proceedings of the 1998 American control reference, Philadelphia, Pennsylvania, pp 2829–2831

  20. Yang GH, Wang JL (2001) Non-fragile H ∞ control for linear systems with multiplicative controller gain variations. Automatica 37(5):727–737

    MathSciNet  Google Scholar 

  21. Du HP, Lam J, Sze KY (2003) Non-fragile output feedback H ∞ vehicle suspension control using genetic algorithm. Eng Appl Artif Intell 16(7-8):667–680

    Article  Google Scholar 

  22. Lien CH (2007) H ∞ non-fragile observer-based controls of dynamical systems via LMI optimization approach. Chaos Solitons Fractals 34(2):428–436

    Article  MathSciNet  Google Scholar 

  23. Lien CH, Cheng WC, Tsai CH, Yu KW (2007) Non-fragile observer-based controls of linear system via LMI approach. Chaos Solitons Fractals 32(4):1530–1537

    Article  MathSciNet  Google Scholar 

  24. Chen JD, Yang CD, Lien CH, Horng JH (2008) New delay-dependent non-fragile H ∞ observer-based control for continuous time-delay systems. Inf Sci 178(21):4699–4706

    Article  MathSciNet  Google Scholar 

  25. Xu SY, Lam J, Yang GH, Wang JL (2006) Stabilization and H ∞ control for uncertain stochastic time-delay systems via non-fragile controllers. Asian J Control 8(2):199–200

    MathSciNet  Google Scholar 

  26. Kang Y, Xiao XB, Xi HS, Ji HB, Wang J (2004) Robust and non-fragile H ∞ control for a class of uncertain hybrid linear systems with Markovian jumping parameters. In: Proceedings of the 5th world congress on intelligent control and automation, June 15–19, Hangzhou, China, pp 1099–1103

  27. Tian X, Xie L, Chen YW (2007) Robust non-fragile H ∞ control for uncertain time delayed stochastic systems with sector constraints. In: 2007 IEEE international conference on control and automation, Guangzhou, China, pp 1852–1856

  28. Trinh H, Fernando T, Nahavandi S (2006) Partial-state observers for nonlinear systems. IEEE Trans Autom Control 51(11):1808–1812

    Article  MathSciNet  Google Scholar 

  29. Busawon KK, Saif M (1999) A state observer for nonlinear systems. IEEE Trans Autom Control 44(11):2098–2103

    Article  MathSciNet  Google Scholar 

  30. Gu DW, Poon FW (2001) A robust state observer scheme. IEEE Trans Autom Control 46(12):1958–1963

    Article  MathSciNet  Google Scholar 

  31. Lien CH (2004) Robust observer-based control of systems with state perturbations via LMI approach. IEEE Trans Autom Control 49(12):1365–1370

    Article  MathSciNet  Google Scholar 

  32. Lien CH (2005) H ∞ observer-based controls for a class of uncertain neutral time-delay systems. J Optim Theory Appl 127(1):129–144

    Article  MathSciNet  Google Scholar 

  33. Lien CH (2006) Delay-dependent H ∞ observer-based control for uncertain neutral systems via LMI approach. J Chin Inst Eng 29(5):801–811

    Article  MathSciNet  Google Scholar 

  34. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference on decision and control, December 2000, Sydney, Australia, pp 2805–2810

  35. Xie LH (1996) Output feedback H-infinite control of systems with parameter uncertainty. Int J Control 63(4):741–750

    Article  Google Scholar 

  36. Mao X (1997) Stochastic differential equations and their applications. Horwood Publications, Chichester

    Google Scholar 

Download references

Acknowledgments

This work reported here was supported by the National Natural Science Foundation of China with Grant Nos. 60874031 and 60904060.

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Authors and Affiliations

  1. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science & Technology, 430081, Wuhan, China

    Guici Chen

  2. Department of Control Science and Engineering, Huazhong University of Science & Technology, 430074, Wuhan, China

    Guici Chen, Yi Shen & Song Zhu

Authors
  1. Guici Chen
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  2. Yi Shen
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  3. Song Zhu
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Correspondence to Guici Chen.

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Chen, G., Shen, Y. & Zhu, S. Non-fragile observer-based H ∞ control for neutral stochastic hybrid systems with time-varying delay. Neural Comput & Applic 20, 1149–1158 (2011). https://doi.org/10.1007/s00521-010-0471-8

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  • DOI: https://doi.org/10.1007/s00521-010-0471-8

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