Skip to main content

Advertisement

SpringerLink
Log in

Further results on memory control of nonlinear discrete-time networked control systems with random input delay

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper is concerned with the problem of memory state feedback stabilization for a class of nonlinear discrete-time networked control systems with partly known probability distribution of input delay. Different from the common assumptions on the delay in the existing literatures, it is assumed that the probabilities of the delay taking values in a finite set are partly known or fully known in advance. In terms of the information about the occurrence probabilities of the delay taking values in the two finite sets, a new stochastic delay model is proposed, where the probability information of the delay is included in the parameter matrices of the transformed system. Based on the new model, a delay-dependent stabilization criterion is derived using a combination of the Lyapunov functional method, convexity of matrix inequalities, and linear matrix inequality technique. Finally, three illustrative examples are provided to show the effectiveness and applicability of the developed theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Azuma, T., Ikeda, K., Kondo, T., Uchida, K.: Memory state feedback control synthesis for linear systems with time delay via a finite number of linear matrix inequalities. Comput. Electr. Eng. 28(3), 217–228 (2002)

    Article  MATH  Google Scholar 

  2. Cao, Y.Y., Frank, P.M.: Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst. 8(2), 200–211 (2000)

    Article  Google Scholar 

  3. Cao, Y.Y., Frank, P.M.: Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst. 124(2), 213–229 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, B., Lam, J., Xu, S.: Memory state feedback guaranteed cost control for neutral delay systems. Int. J. Innov. Comput. Inf. Control 2(2), 293–303 (2006)

    Google Scholar 

  5. Chen, B., Liu, X., Tong, S.: Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay. Fuzzy Sets Syst. 157(16), 2224–2240 (2006)

    Google Scholar 

  6. Chen, B., Liu, X.P., Tong, S.C., Lin, C.: Observer-based stabilization of t-s fuzzy systems with input delay. IEEE Trans. Fuzzy Syst. 16(3), 652–663 (2008)

    Article  Google Scholar 

  7. Chen, B., Liu, X., Lin, C., Liu, K.: Robust \(H_{\infty }\) control of Takagi–Sugeno fuzzy systems with state and input time delays. Fuzzy Sets Syst. 160(4), 403–422 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fridman, E., Shaked, U.: Stability and guaranteed cost control of uncertain discrete delay systems. Int. J. Control 78(4), 235–246 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gao, H., Wang, C.: Comments and further results on a descriptor system approach to h1 control of linear time-delay systems. IEEE Trans. Autom. Control 48(3), 520–525 (2003)

    Article  Google Scholar 

  10. Gao, H., Lam, J., Wang, C., Wang, Y.: Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proc. Control Theory Appl. 151(6), 691–698 (2004)

    Article  MathSciNet  Google Scholar 

  11. Gao, H., Chen, T.: New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control 52(2), 328–334 (2007)

    Article  MathSciNet  Google Scholar 

  12. Gao, H., Meng, X., Chen, T.: Stabilization of networked control systems with a new delay characterization. IEEE Trans. Autom. Control 53(9), 2142–2148 (2008)

    Article  MathSciNet  Google Scholar 

  13. Gao, H., Zhao, Y., Chen, T.: \(H_{\infty }\) fuzzy control of nonlinear systems under unreliable communication links. IEEE Trans. Fuzzy Syst. 17(2), 265–278 (2009)

    Article  Google Scholar 

  14. El Ghaoui, L., Oustry, F., AitRami, M.: A cone complementarity linearization algorithm for static output–feedback and related problems. IEEE Trans. Autom. Control 42(8), 1171–1176 (1997)

    Google Scholar 

  15. Gu, K., Chen, J., Kharitonov, V.L.: Stability of Time Delay Systems. Springer, New York (2003)

    Book  MATH  Google Scholar 

  16. Hu, S., Liu, J.: Stabilization of discrete-time T-S fuzzy systems with random input delay: a new modeling method. In: IEEE Control and Decision Conference (CCDC), 2010 Chinese, pp. 1243–1248 (2010).

  17. Jiang, X., Han, Q.L.: Robust \(H_{\infty }\) control for uncertain Takagi–Sugeno fuzzy systems with interval time-varying delay. IEEE Trans. Fuzzy Syst. 15(2), 321–331 (2007)

    Article  Google Scholar 

  18. Kim, D.S., Lee, Y.S., Kwon, W.H., Park, H.S.: Maximum allowable delay bounds of networked control systems. Control Eng. Pract. 11(11), 1301–1313 (2003)

    Article  Google Scholar 

  19. Kim, S.H.: T–S fuzzy control design for a class of nonlinear networked control systems. Nonlinear Dyn. 73(1–2), 17–27 (2013)

    Article  MATH  Google Scholar 

  20. Knightly, E.W.: A new approach to providing statistical performance guarantees to vbr traffic. In: Proceedings of the Fifteenth Annual Joint Conference of the IEEE Computer Societies. Networking the Next Generation, vol. 3, pp. 1091–1099 (1996).

  21. Lee, T.H., Park, J.H., Kwon, O., Lee, S.: Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw. 46, 99–108 (2013)

    Article  Google Scholar 

  22. Lee, T.H., Park, J.H., Lee, S., Kwon, O.: Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int. J. Control 86(1), 107–119 (2013)

    Google Scholar 

  23. Liu, J., Gu, Z., Han, H., Hu, S.: T–S fuzzy model-based memory control for discrete-time system with random input delay. Iran. J. Fuzzy Syst. 8(3), 67–79 (2011)

    MATH  MathSciNet  Google Scholar 

  24. Moon, Y., Park, P., Kwon, W., Lee, Y.: Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74(14), 1447–1455 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  25. Takagy, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)

    Article  Google Scholar 

  26. Tian, E., Yue, D., Wang, Z.: Robust \(H_{\infty }\) control for uncertain discrete-time systems with probabilistic state delays. Asian J. Control 11(5), 503–516 (2009)

    Article  MathSciNet  Google Scholar 

  27. Wang, S., Nathuji, R., Bettati, R., Zhao, W.: Providing statistical delay guarantees in wireless networks. In: Proceedings of the 24th International Conference on Distributed Computing Systems, pp. 48–55 (2004).

  28. Wang, Z., Lam, J., Burnham, K.J.: Stability analysis and observer design for neutral delay systems. IEEE Trans. Autom. Control 47(3), 478–483 (2002)

    Article  MathSciNet  Google Scholar 

  29. Xu, S., Lam, J.: Improved delay-dependent stability criteria for time-delay systems. IEEE Trans. Autom. Control 50(3), 384–387 (2005)

    Article  MathSciNet  Google Scholar 

  30. Yi, Z., Heng, P.A.: Stability of fuzzy control systems with bounded uncertain delays. IEEE Trans. Fuzzy Syst. 10(1), 92–97 (2002)

    Article  MATH  Google Scholar 

  31. Yue, D., Lam, J.: Reliable memory feedback design for a class of non-linear time-delay systems. Int. J. Robust Nonlinear Control 14(1), 39–60 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  32. Yue, D., Han, Q.L., Lam, J.: Network-based robust \(H_{\infty }\) control of systems with uncertainty. Automatica 41(6), 999–1007 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  33. Yue, D., Tian, E., Wang, Z., Lam, J.: Stabilization of systems with probabilistic interval input delays and its applications to networked control systems. IEEE Trans. Syst. Man Cybern. A 39(4), 939–945 (2009)

    Article  Google Scholar 

  34. Yue, D., Tian, E., Zhang, Y., Peng, C.: Delay-distribution-dependent stability and stabilization of T–S fuzzy systems with probabilistic interval delay. IEEE Trans. Syst. Man Cybern. B 39(2), 503–516 (2009)

    Article  Google Scholar 

  35. Yun, S.W., Choi, Y.J., Park, P.: Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization. Nonlinear Dyn. 62(1–2), 95–104 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  36. Zhang, L., Shi, Y., Chen, T., Huang, B.: A new method for stabilization of networked control systems with random delays. IEEE Trans. Autom. Control 50(8), 1177–1181 (2005)

    Article  MathSciNet  Google Scholar 

  37. Zhang, X.M., Wu, M., She, J.H., He, Y.: Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica 41(8), 1405–1412 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  38. Zheng, F., Cheng, M., Gao, W.B.: Variable structure control of time-delay systems with a simulation study on stabilizing combustion in liquid propellant rocket motors. Automatica 31(7), 1031–1037 (1995)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61304043 and No. 51379170), the Fundamental Research Funds for the Central Universities (WUT: 2013-IV-105), the Nanjing University of Posts and Telecommunications Talent Introduction Foundation, China (Grant No. NY213089), and the Open-end Funds of the Institute of Advanced Technology, Nanjing University of Posts and Telecommunications.

Author information

Authors and Affiliations

  1. College of Automation and Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Songlin Hu

  2. Department of Control Science and Engineering and the Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Xiuxia Yin & Yunning Zhang

  3. Hubei Key Laboratory of Inland Shipping Technology, School of Navigation, Wuhan University of Technology, Wuhan,  430063, Hubei, People’s Republic of China

    Yong Ma

Authors
  1. Songlin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiuxia Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yunning Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yong Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Ma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, S., Yin, X., Zhang, Y. et al. Further results on memory control of nonlinear discrete-time networked control systems with random input delay. Nonlinear Dyn 77, 1531–1545 (2014). https://doi.org/10.1007/s11071-014-1397-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1397-y

Keywords

Search

Navigation