Skip to main content
SpringerLink
Log in

Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays

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

Abstract

This paper addresses the problem of finite-time observer-based control for continuous-time nonlinear Markovian jump systems with time-varying delays. The existing studies about asynchronous observer-based control for Markovian jump systems in continuous-time case only consider the asynchronism of controller and original system, but suppose that the observer and original system are switched with the same Markovian process, which is unreasonable in practice. In this paper, the modes of observer and controller are supposed to be asynchronous with the modes of original system simultaneously. Firstly, by constructing novel Lyapunov–Krasovskii functionals and using finite-time analysis theory, the error system is proved to be finite-time bounded with an \(H_\infty \) performance level. Secondly, the parameters of desired observer and controller are calculated by virtue of linear matrix inequalities. Finally, two numerical examples are provided to illustrate the less conservativeness and effectiveness of our proposed method.

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

Similar content being viewed by others

References

  1. Bolzern, P., Colaneri, P., De Nicolao, G.: Stochastic stability of positive Markov jump linear systems. Automatica 50(4), 1181–1187 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Chen, L., Zhao, Y., Fu, S., Liu, M., Qiu, J.: Fault estimation observer design for descriptor switched systems with actuator and sensor failures. IEEE Trans. Circuits Syst. I Regul. Pap. 66(2), 810–819 (2018)

    MathSciNet  Google Scholar 

  3. Chen, M., Yang, X., Shen, H., Yao, F.: Finite-time asynchronous \(H_\infty \) control for Markov jump repeated scalar non-linear systems with input constraints. Appl. Math. Comput. 275, 172–180 (2016)

    MathSciNet  MATH  Google Scholar 

  4. Cheng, J., Ahn, C.K., Karimi, H.R., Cao, J., Qi, W.: An event-based asynchronous approach to Markov jump systems with hidden mode detections and missing measurements. IEEE Trans. Syst. Man Cybern. Syst. 49(9), 1749–1758 (2019)

    Google Scholar 

  5. Cheng, P., He, S.: Observer-based finite-time asynchronous control for a class of hidden Markov jumping systems with conic-type non-linearities. IET Control Theory Appl. 14(2), 244–252 (2019)

    Google Scholar 

  6. Cui, G., Yu, J., Wang, Q.: Finite-time adaptive fuzzy control for MIMO nonlinear systems with input saturation via improved command-filtered backstepping. IEEE Trans. Syst. Man Cybern. Syst. (Early Access) https://doi.org/10.1109/TSMC.2020.3010642

  7. do Valle Costa, O.L., Fragoso, M.D., Todorov, M.G.: Continuous-Time Markov Jump Linear Systems. Springer, Berlin (2012)

    MATH  Google Scholar 

  8. Dong, S., Wu, Z., Su, H., Shi, P., Karimi, H.R.: Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity. IEEE Trans. Autom. Control 64(3), 1250–1256 (2019)

    MathSciNet  MATH  Google Scholar 

  9. Dorato, P.: Short time stability in linear time-varying systems. In: Proceedings of the IRE International Convention Record Part, vol. 4, pp. 83–87 (1961)

  10. Fang, M., Dong, S., Wu, Z.: Asynchronous \(H_\infty \) filtering of continuous-time Markov jump systems. Int. J. Robust Nonlinear Control 30(2), 685–698 (2020)

    MathSciNet  MATH  Google Scholar 

  11. Faraji Niri, M.: Robust non-fragile asynchronous controller design for continuous-time Markov jump linear systems: non-homogeneous Markov process approach. Circuits Syst. Signal Process. 37(10), 4234–4255 (2018)

    MathSciNet  Google Scholar 

  12. Guo, Y.: Stabilization of positive Markov jump systems. J. Frankl. Inst. 353(14), 3428–3440 (2016)

    MathSciNet  MATH  Google Scholar 

  13. He, S., Liu, F.: Observer-based finite-time control of time-delayed jump systems. Appl. Math. Comput. 217, 2327–2338 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Kim, S., Park, P., Jeong, C.: Robust \(H_\infty \) stabilisation of networked control systems with packet analyser. IET Control Theory Appl. 4(9), 1828–1837 (2010)

    Google Scholar 

  15. Li, F., Du, C., Yang, C., Gui, W.: Passivity-based asynchronous sliding mode control for delayed singular Markovian jump systems. IEEE Trans. Autom. Control 63(8), 2715–2721 (2017)

    MathSciNet  MATH  Google Scholar 

  16. Li, H., Shi, P., Yao, D.: Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults. IEEE Trans. Automat. Control 62(4), 1933–1939 (2017)

    MathSciNet  MATH  Google Scholar 

  17. Li, J., Shen, L., Yao, F., Zhao, H., Wang, J.: An event-triggered approach to finite-time observer-based control for Markov jump systems with repeated scalar nonlinearities. Trans. Inst. Meas. Control 40(9), 2789–2797 (2018)

    Google Scholar 

  18. Li, M., Chen, X., Liu, M., Zhang, Y., Zhang, H.: Asynchronous adaptive fault-tolerant sliding-mode control for T-S fuzzy singular Markovian jump systems with uncertain transition rates. IEEE Trans. Cybern. (Early Access) (2020). https://doi.org/10.1109/TCYB.2020.2981158

  19. Li, X., Ahn, C.K., Lu, D., Guo, S.: Robust simultaneous fault estimation and nonfragile output feedback fault-tolerant control for Markovian jump systems. IEEE Trans. Syst. Man Cybern. Syst. 49(9), 1769–1776 (2019)

    Google Scholar 

  20. Liu, W., Shi, P., Pan, J.S.: State estimation for discrete-time Markov jump linear systems with time-correlated and mode-dependent measurement noise. Automatica 85, 9–21 (2017)

    MathSciNet  MATH  Google Scholar 

  21. Ma, Q., Xu, S.: Consensus switching of second-order multiagent systems with time delay. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3011448

    Article  Google Scholar 

  22. Ma, Y., Jia, X., Yan, Y., Liu, D.: Observer-based \(H_\infty \) control for nonlinear Markovian jump systems with time-delay and input saturation. Comput. Appl. Math. 37(1), 1–21 (2018)

    MathSciNet  MATH  Google Scholar 

  23. Qiu, J., Wei, Y., Karimi, H.R.: New approach to delay-dependent \(H_\infty \) control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. J. Frankl. Inst. 352(1), 189–215 (2015)

    MATH  Google Scholar 

  24. Ren, H., Zong, G., Li, T.: Event-triggered finite-time control for networked switched linear systems with asynchronous switching. IEEE Trans. Syst. Man Cybern. 48(11), 1874–1884 (2018)

    Google Scholar 

  25. Shen, H., Park, J.H., Wu, Z.: Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn. 77(4), 1709–1720 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Shen, H., Wu, Z., Park, J.H.: Reliable mixed passive and \(H_\infty \) filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures. Int. J. Robust Nonlinear Control 25(17), 3231–3251 (2015)

    MathSciNet  MATH  Google Scholar 

  27. Shen, Y., Wu, Z., Shi, P., Shu, Z., Karimi, H.R.: \(H_\infty \) control of Markov jump time-delay systems under asynchronous controller and quantizer. Automatica 99, 352–360 (2019)

    MathSciNet  MATH  Google Scholar 

  28. Song, J., Niu, Y., Zou, Y.: Asynchronous output feedback control of time-varying Markovian jump systems within a finite-time interval. J. Frankl. Inst. 354(15), 6747–6765 (2017)

    MathSciNet  MATH  Google Scholar 

  29. Song, X., Wang, M., Ahn, C.K., Song, S.: Finite-time \(H_\infty \) asynchronous control for nonlinear Markov jump distributed parameter systems via quantized fuzzy output-feedback approach. IEEE Trans. Cybern. 2019, 1–12 (2019)

    Google Scholar 

  30. Tian, Y., Wang, Z.: Extended dissipativity analysis for Markovian jump neural networks via double-integral-based delay-product-type Lyapunov functional. IEEE Trans. Neural Netw. Learn. Syst. (2020). https://doi.org/10.1109/TNNLS.2020.3008691

    Article  Google Scholar 

  31. Tian, Y., Wang, Z.: Finite-time extended dissipative filtering for singular T-S fuzzy systems with nonhomogeneous Markov jumps. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3030503

  32. Tian, Y., Wang, Z.: A new multiple integral inequality and its application to stability analysis of time-delay systems. Appl. Math. Lett. 105, 106325 (2020)

    MathSciNet  MATH  Google Scholar 

  33. Wang, T., Tong, S.: Observer-based output-feedback asynchronous control for switched fuzzy systems. IEEE Trans. Syst. Man Cybern. 47(9), 2579–2591 (2016)

    Google Scholar 

  34. Wang, Y., Chen, F., Zhuang, G.: Dynamic event-based reliable dissipative asynchronous control for stochastic markov jump systems with general conditional probabilities. Nonlinear Dyn. 101, 465–485 (2020)

    Google Scholar 

  35. Wang, Y., Xu, S., Li, Y., Chu, Y., Zhang, Z.: Asynchronous finite-time state estimation for semi-Markovian jump neural networks with randomly occurred sensor nonlinearities. Neurocomputing 432, 240–249 (2021)

    Google Scholar 

  36. Weiss, L., Infante, E.: On the stability of systems defined over a finite time interval. Proc. Natl. Acad. Sci. 54(1), 44–48 (1965)

    MathSciNet  MATH  Google Scholar 

  37. Weiss, L., Infante, E.: Finite time stability under perturbing forces and on product spaces. IEEE Trans. Autom. Control 12(1), 54–59 (1967)

    MathSciNet  MATH  Google Scholar 

  38. Wu, H.: Reliable robust \(H_\infty \) fuzzy control for uncertain nonlinear systems with Markovian jumping actuator faults. J. Dyn. Syst. Meas. Control 129(3), 252–261 (2007)

    Google Scholar 

  39. Wu, Z., Shi, P., Shu, Z., Su, H., Lu, R.: Passivity-based asynchronous control for Markov jump systems. IEEE Trans. Automat. Control 62(4), 2020–2025 (2016)

    MathSciNet  MATH  Google Scholar 

  40. Xu, S., Lam, J., Mao, X.: Delay-dependent \(H_\infty \) control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. I: Reg. Pap. 54(9), 2070–2077 (2007)

    MathSciNet  MATH  Google Scholar 

  41. Yin, Y., Shi, P., Liu, F., Teo, K.L.: Fuzzy model-based robust \(H_\infty \) filtering for a class of nonlinear nonhomogeneous Markov jump systems. Signal Process. 93(9), 2381–2391 (2013)

    Google Scholar 

  42. Yu, P., Ma, Y.: Observer-based asynchronous control for Markov jump systems. Appl. Math. Comput. 377, 125184 (2020)

    MathSciNet  MATH  Google Scholar 

  43. Zhang, B., Zheng, W.X., Xu, S.: Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans. Circuits Syst. I Reg. Pap. 60(5), 1250–1263 (2013)

    MathSciNet  Google Scholar 

  44. Zhang, C., Long, F., He, Y., Yao, W., Jiang, L., Wu, M.: A relaxed quadratic function negative-determination lemma and its application to time-delay systems. Automatica 113, 108764 (2020)

    MathSciNet  MATH  Google Scholar 

  45. Zhang, L., Leng, Y., Colaneri, P.: Stability and stabilization of discrete-time semi-Markov jump linear systems via semi-Markov kernel approach. IEEE Trans. Autom. Control 61(2), 503–508 (2016)

    MathSciNet  MATH  Google Scholar 

  46. Zhang, M., Shen, C., Wu, Z.: Asynchronous observer-based control for exponential stabilization of Markov jump systems. IEEE Trans. Circuits Syst. II, Express Briefs 67(10), 2039–2043 (2019)

    Google Scholar 

  47. Zhao, X., Zeng, Q.: Delay-dependent \(H_\infty \) performance analysis and filtering for Markovian jump systems with interval time-varying delays. Int. J. Adapt. Control Signal Process. 24(8), 633–642 (2010)

    MathSciNet  MATH  Google Scholar 

  48. Zong, G., Ren, H.: Guaranteed cost finite-time control for semi-Markov jump systems with event-triggered scheme and quantization input. Int. J. Robust Nonlinear Control 29(15), 5251–5273 (2019)

    MathSciNet  MATH  Google Scholar 

  49. Zong, G., Yang, D., Hou, L., Wang, Q.: Robust finite-time \(H_\infty \) control for Markovian jump systems with partially known transition probabilities. J. Frankl. Inst. 350(6), 1562–1578 (2013)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the NSFC 62073166, 61673215, the 333 Project (BRA2017380), a project funded by the Priority Academic Program Development of Jiangsu, the Key Laboratory of Jiangsu Province.

Author information

Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yao Wang & Shengyuan Xu

  2. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210023, China

    Junwei Lu

  3. School of Electrical Engineering and Automation, Qufu Normal University, Rizhao, 276826, China

    Zhengqiang Zhang

Authors
  1. Yao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengyuan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junwei Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhengqiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengyuan Xu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Xu, S., Lu, J. et al. Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays. Nonlinear Dyn 104, 509–521 (2021). https://doi.org/10.1007/s11071-021-06307-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06307-4

Keywords

Search

Navigation