Skip to main content
SpringerLink
Log in

Fault detection filter design for a class of nonlinear Markovian jumping systems with mode-dependent time-varying delays

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

Abstract

The fault detection filter (FDF) design problem of a class of time-delayed and nonlinear Markovian jumping systems (MJSs) is considered. The delays in this paper are mode-dependent and time-varying. Using the Takagi–Sugeno fuzzy (TSF) modeling methods, the relevant TSF-MJSs related to the TSF-FDF model are obtained. Through introducing a reference residual model, the FDF design scheme can be derived as an \(H_{\infty }\)-filtering formulation. By selecting a suitable mode-dependent time-delayed Lyapunov–Krasovskii functional (LKF), we get sufficient conditions through which the stochastic stability of the TSF-MJSs can be guaranteed. Then in terms of linear matrix inequalities techniques, the fuzzy FDF design scheme can be derived as an optimization one. A simulation example is demonstrated as last to illustrate the feasibility of the studied methods.

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

Similar content being viewed by others

References

  1. Zuo, Z., Lin, Z., Ding, Z.: Truncated prediction output feedback control of a class of Lipschitz nonlinear systems with input delay. IEEE Trans. Circuits Syst. II Express Briefs 63(8), 788–792 (2016)

    Article  Google Scholar 

  2. Wu, Z., Shi, P., Su, H., Chu, J.: Asynchronous \(L_{2}-L_{\infty }\) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica 50(1), 180–186 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. He, S., Song, J., Liu, F.: Robust finite-time bounded controller design of time-delay conic nonlinear systems using sliding mode control strategy. IEEE Trans. Syst. Man Cybern. Syst. https://doi.org/10.1109/TFUZZ.2016.2633325 (2017) (in press)

  4. Takagi, 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  MATH  Google Scholar 

  5. Shen, M., Ye, D.: Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions. Fuzzy Sets Syst. 217(9), 80–95 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shen, H., Zhu, Y., Zhang, L., Park, J.H.: Extended dissipative state estimation for Markov jump neural networks with unreliable links. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 346–358 (2017)

    Article  MathSciNet  Google Scholar 

  7. Cheng, J., Park, J.H., Zhang, L., Zhu, Y.: An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies. IEEE Trans. Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2016.2633325 (2017) (in press)

  8. Doha, E.H., Ahmed, E.H., Roger, C.: Finite frequency \(H_{\infty }\) filter design for T–S fuzzy systems: new approach. Signal Process. 143, 191–199 (2018)

    Article  Google Scholar 

  9. Choon, K.A.: Delay-dependent state estimation for T–S fuzzy delayed Hopfield neural networks. Nonlinear Dyn. 61(3), 483–489 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mao, M.: Stability of stochastic differential equations with Markovian switching. Stoch. Process. Appl. 79(1), 45–67 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Feng, X., Loparo, K.A., Ji, Y.: Stochastic stability properties of jump linear systems. IEEE Trans. Autom. Control 37(1), 38–53 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Antonio, S., Manuel, H.M., Carlos, A.: Stable receding-horizon scenario predictive control for Markov-jump linear systems. Automatica 86, 121–128 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sivaranjani, K., Rakkiyappan, R.: Delayed impulsive synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations. Nonlinear Dyn. 88(3), 1917–1934 (2017)

    Article  Google Scholar 

  14. Balasubramaniam, P., Lakshmanan, S., Theesar, S.J.S.: State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60(4), 661–675 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Li, J., Zhang, Q., Zhai, D., Zhang, Y.: Sliding mode control for descriptor Markovian jump systems with mode-dependent derivative-term coefficient. Nonlinear Dyn. 82(1), 465–480 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, Z., Lam, J., Liu, X.: Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances. IEEE Trans. Circuits Syst. II Express Briefs 51(5), 262–268 (2004)

    Article  Google Scholar 

  17. Xu, Y., Lu, R., Shi, P., Tao, J., Xie, S.: Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling. IEEE Trans. Neural Netw. Learn. Syst. https://doi.org/10.1109/TNNLS.2016.2636325 (2017) (in press)

  18. Wang, J., Yang, G., Liu, J.: An LMI approach to \(H_index\) and mixed \(H_/H_{\infty }\) fault detection observer design. Automatica 43, 1656–1665 (2007)

    Article  MathSciNet  Google Scholar 

  19. Sohag, K.: An overview of fault tree analysis and its application in model based dependability analysis. Expert Syst. Appl. 77, 114–135 (2017)

    Article  Google Scholar 

  20. Maryam, S., Farid, S., Javad, A.: Adaptive fault detection and estimation scheme for a class of uncertain nonlinear systems. Nonlinear Dyn. 79(4), 2623–2637 (2015)

    Article  MathSciNet  Google Scholar 

  21. Zhong, M., Ding, S.X., Lam, J., Wang, B.: An LMI approach to design robust fault detection filter for uncertain LTI systems. Automatica 39(3), 543–550 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Park, B.S., Yoo, S.J.: Fault detection and accommodation of saturated actuators for underactuated surface vessels in the presence of nonlinear uncertainties. Nonlinear Dyn. 85(2), 1067–1077 (2016)

    Article  MATH  Google Scholar 

  23. Nguang, S.K., Shi, P., Ding, S.: Fault detection for uncertain fuzzy systems: an LMI approach. IEEE Trans. Fuzzy Syst. 15(6), 1251–1262 (2007)

    Article  Google Scholar 

  24. Altaf, U., Khan, A.Q., Mustafa, G., Raza, M.T., Abid, M.: Design of robust \(H_{\infty }\) fault detection filter for uncertain time-delay systems using canonical form approach. J. Franklin Inst. 353(1), 54–71 (2010)

    Article  Google Scholar 

  25. Li, H., Chen, Z., Wu, L., Lam, H. K., Du, H.: Event-triggered fault detection of nonlinear networked systems. IEEE Trans. Cybern. https://doi.org/10.1109/TCYB.2016.2536750 (2017) (in press)

  26. Zhong, M., Ye, H., Shi, P., Wang, G.: Fault detection for Markovian jump systems. IEE Proc. Control Theory Appl. 152(4), 397–402 (2005)

    Article  Google Scholar 

  27. Hibey, J.L., Charalambous, C.D.: Conditional densities for continuous-time nonlinear hybrid systems with applications to fault detection. IEEE Trans. Autom. Control 44(11), 2164–2169 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  28. He, S., Liu, F.: Fuzzy model-based fault detection for Markov jump systems. Int. J. Robust Nonlinear Control 19(10), 1248–1266 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Meskin, N., Khorasani, K.: Fault detection and isolation of discrete-time Markovian jump linear systems with application to a network of multi-agent systems having imperfect communication channels. Automatica 45(9), 2032–2040 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Luo, M., Liu, G., Zhong, S.: Robust fault detection of Markovian jump systems with different system modes. Appl. Math. Model. 37(7), 5001–5012 (2013)

    Article  MathSciNet  Google Scholar 

  31. Zhai, D., An, L., Li, J., Zhang, Q.: Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time. Appl. Math. Comput. 273, 767–792 (2016)

    MathSciNet  Google Scholar 

  32. Hamed, H., Ian, H., Reza, H.: Bayesian sensor fault detection in a Markov jump system. Asian J. Control 19(4), 1465–1481 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. Gagliardi, G., Casavola, A., Famularo, D.: A fault detection and isolation filter design method for Markov jump linear parameter-varying systems. Int. J. Adapt. Control Signal Process. 26(3), 241–257 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  34. Saijai, J., Ding, S.X., Abdo, A., Shen, B., Damlakhi, W.: Threshold computation for fault detection in linear discrete-time Markov jump systems. Int. J. Adapt. Control Signal Process. 28(11), 1106–1127 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  35. Luo, M., Zhong, S.: Passivity analysis and passification of uncertain Markovian jump systems with partially known transition rates and mode-dependent interval time-varying delays. Comput. Math. Appl. 63, 1266–1278 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wang, Y., Ren, W., Lu, Y.: Nonfragile \(H_{\infty }\) filtering for nonlinear Markovian jumping systems with mode-dependent time delays and quantization. J. Control Sci. Eng. Article ID 7167692 (2016)

  37. He, S., Xu, H.: Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach. Nonlinear Dyn. 80(3), 1159–1171 (2015)

    Article  MATH  Google Scholar 

  38. Wang, Y., Shen, H., Karimi, H. R., Duan, D.: Dissipativity-based fuzzy integral sliding mode control of continuous-time T–S fuzzy systems. IEEE Trans. Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2710952 (2017) (in press)

  39. He, W., Chen, Y., Yin, Z.: Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans. Cybern. 46(3), 620–629 (2016)

    Article  Google Scholar 

  40. Muthukumar, P., Balasubramaniam, P., Ratnavelu, K.: T–S fuzzy predictive control for fractional order dynamical systems and its applications. Nonlinear Dyn. 86(2), 751–763 (2016)

    Article  MATH  Google Scholar 

  41. Vembarasan, V., Balasubramaniam, P.: Chaotic synchronization of Rikitake system based on T–S fuzzy control techniques. Nonlinear Dyn. 74(1–2), 31–44 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  42. Meskin, N., Khorasani, K.: A geometric approach to fault detection and isolation of continuous-time Markovian jump linear systems. IEEE Trans. Autom. Control 55(6), 1343–1357 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of P. R. China (Nos. 61673001, 61203051, 61573021, 11771001), the Foundation of Distinguished Young Scholars of Anhui Province (No. 1608085J05) and the Key Support Program of University Outstanding Youth Talent of Anhui Province (No. gxydZD201701).

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Shuping He

Authors
  1. Shuping He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuping He.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, S. Fault detection filter design for a class of nonlinear Markovian jumping systems with mode-dependent time-varying delays. Nonlinear Dyn 91, 1871–1884 (2018). https://doi.org/10.1007/s11071-017-3987-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3987-y

Keywords

Search

Navigation