Finite frequency fault detection for a class of nonhomogeneous Markov jump systems with nonlinearities and sensor failures

  • Yue Long
  • Ju H. ParkEmail author
  • Dan Ye
Original Paper


In this paper, the finite frequency fault detection (FD) problem is addressed for a class of nonhomogeneous Markov jump systems with nonlinearities and sensor failures. Compared with the existing sensor fault models that contain many known faulty modes, the fault model in this paper is more general since it not only covers more types of sensor failures but also does not need to know the fault information in advance. Then, by means of finite frequency stochastic performance indices, a novel FD scheme is proposed. Some new lemmas, in which the nonlinear item and nonhomogeneous Markov switching are dealt appropriately, are developed to capture the stability of the system and desired finite frequency performances. Then, by the derived lemmas, sufficient conditions with potentially less conservativeness are investigated to guarantee the existence of the FD filters. Finally, an application to HiMAT vehicle is given to illustrate the effectiveness of the derived theoretical results.


Fault detection Finite frequency Nonhomogeneous Nonlinearities Sensor failure 



This work was supported by 2017 Yeungnam University Research Grant. Also, the work of Y. Long and D. Ye was supported by NSFC (Nos. 61773187, 61773097), the Fundamental Research Funds for the Central Universities (No. N160402004).

Compliance with ethical standards

Conflict of interest

All the authors declare that there are no potential conflicts of interest and approval of the submission.


  1. 1.
    Moon, J., Basar, T.: Risk-sensitive control of Markov jump linear systems: caveats and difficulties. Int. J. Control Autom. Syst. 15(1), 462–467 (2017)Google Scholar
  2. 2.
    Park, J.H., Shen, H., Chang, X.H., Lee, T.H.: Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals. Springer, Cham (2018). Google Scholar
  3. 3.
    Shi, P., Yin, Y.Y., Liu, F., Zhang, J.H.: Robust control on saturated Markov jump systems with missing information. Inf. Sci. 265(1), 123–138 (2014)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Wu, Z.-G., Shi, P., Shu, Z., Su, H.Y., Lu, R.Q.: Passivity-based asynchronous control for Markov jump systems. IEEE Trans. Autom. Control 62(4), 2020–2025 (2017)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Tao, J., Wu, Z.-G., Su, H.Y., Wu, Y.Q., Zhang, D.: Asynchronous and resilient filtering for Markovian jump neural networks subject to extended dissipativity. IEEE Trans. Cybern. (2018)
  6. 6.
    Shen, Y., Wu, Z.-G., Shi, P., Shu, Z., Karimi, H.R.: H-infinity control of Markov jump time-delay systems under asynchronous controller and quantizer. Automatica 99, 352–360 (2019)Google Scholar
  7. 7.
    Shen, H., Park, J.H., Wu, Z.G.: Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn. 77, 1709–1720 (2014)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Qi, W., Kao, Y., Gao, X.: Passivity and passification for stochastic systems with Markovian switching and generally uncertain transition rates. Int. J. Control Autom. Syst. 15, 2174–2181 (2017)Google Scholar
  9. 9.
    Yao, X.M., Guo, L., Wu, L.G., Dong, H.R.: Static anti-windup design for nonlinear Markovian jump systems with multiple disturbances. Inf. Sci. 418(24), 169–183 (2017)Google Scholar
  10. 10.
    Ma, S.P., Boukas, E.K., Chinniah, Y.: Stability and stabilization of discrete-time singular Markov jump systems with time-varying delay. Int. J. Robust Nonlinear Control 20(5), 531–543 (2010)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Zhong, X.N., He, H.B., Zhang, H.G., Wang, Z.S.: Optimal control for unknown discrete-time nonlinear Markov jump systems using adaptive dynamic programming. IEEE Trans. Neural Netw. Learn. Syst. 25(12), 2141–2155 (2014)Google Scholar
  12. 12.
    Lam, J., Shu, Z., Xu, S., Boukas, E.K.: Robust \({\cal{H}}_{\infty }\) control of descriptor discrete-time Markovian jump systems. Int. J. Control 80, 374–385 (2007)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Shi, P., Li, F.B.: A survey on Markovian jump systems: modeling and design. Int. J. Control Autom. Syst. 13(1), 1–16 (2015)MathSciNetGoogle Scholar
  14. 14.
    Zhang, L.X., Boukas, E.K.: Stability and stabilization of Markovian jump linear systems with partly unknown transition probability. Automatica 45(2), 463–468 (2009)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Liu, X.H., Yu, X.H., Ma, G.Q., Xi, H.S.: On sliding mode control for networked control systems with semi-Markovian switching and random sensor delays. Inf. Sci. 337–338, 44–58 (2016)zbMATHGoogle Scholar
  16. 16.
    Zhang, L.X.: \({\cal{H}}_{\infty }\) estimation for discrete-time piecewise homogeneous Markov jump linear systems. Automatica 45, 2570–2576 (2009)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Yin, Y.Y., Shi, P., Liu, F., Teo, K.L.: Filtering for discrete-time nonhomogeneous Markov jump systems witn uncertainties. Inf. Sci. 259(20), 118–127 (2014)zbMATHGoogle Scholar
  18. 18.
    Li, X.-J., Yang, G.-H.: Fault detection in finite frequency domain for Takagi–Sugeno fuzzy systems with sensor faults. IEEE Trans. Cybern. 44(8), 1446–1458 (2014)Google Scholar
  19. 19.
    Zhao, D., Wang, Y.Q., Li, Y.Y., Ding, S.X.: \({\cal{H}}_{\infty }\) fault estimation for two-dimensional linear discrete time-varying systems based on Krein space method. IEEE Trans. Syst. Man Cybern. Syst. 48(12), 2070–2079 (2018)Google Scholar
  20. 20.
    Li, Y.Y., Karimi, H.R., Zhang, Q., Zhao, D., Li, Y.B.: Fault detection for linear discrete time-varying systems subject to random sensor delay: a Riccati equation approach. IEEE Trans. Circuits Syst. Regul. Pap. 65(5), 1707–1716 (2018)Google Scholar
  21. 21.
    Park, J.H., Mathiyalagan, K., Sakthivel, R.: Fault estimation for discrete-time switched nonlinear systems with discrete and distributed time varying delays. Int. J. Robust Nonlinear Control 26, 3755–3771 (2016)zbMATHGoogle Scholar
  22. 22.
    Du, D., Xu, S.: Actuator fault detection for discrete-time switched linear systems with output disturbance. Int. J. Control Autom. Syst. 15, 2590–2598 (2017)Google Scholar
  23. 23.
    Wu, L.G., Yao, X.M., Zheng, W.X.: Generalized \({\cal{H}}_{2}\) fault detection for two-dimensional Markovian jump systems. Automatica 48(8), 1741–1750 (2012)MathSciNetzbMATHGoogle Scholar
  24. 24.
    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)MathSciNetzbMATHGoogle Scholar
  25. 25.
    He, S.P., Liu, F.: Fuzzy model-based fault detection for Markov jump systems. Int. J. Robust Nonlinear Control 19(11), 1248–1266 (2009)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Dong, H.L., Wang, Z.D., Gao, H.J.: Fault detection for Markovian jump systems with sensor saturations and randomly varying nonlinearities. IEEE Trans. Circuits Syst. I Regul. Pap. 59(10), 2354–2362 (2012)MathSciNetGoogle Scholar
  27. 27.
    Iwasaki, T., Hara, S.: Generalized KYP lemma: unified frequency domain inequalities with design applications. IEEE Trans. Autom. Control 50(1), 41–59 (2005)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Wang, H., Yang, G.-H.: A finite frequency approach to filter design for uncertain discrete-time systems. Int. J. Adapt. Control Signal Process. 22, 533–553 (2008)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Wang, H., Yang, G.-H.: Integrated fault detection and control for LPV systems. Int. J. Robust Nonlinear Control 19, 341–363 (2009)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Yang, G.-H., Wang, H., Xie, L.H.: Fault detection for output feedback control systems with actuator stuck faults: a steady-state-based approach. Int. J. Robust Nonlinear Control 20, 1739–1757 (2010)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Long, Y., Park, J.H., Ye, D.: Transmission-dependent fault detection and isolation strategy for networked systems under finite capacity channels. IEEE Trans. Cybern. 47(8), 2266–2278 (2017)Google Scholar
  32. 32.
    Hou, Y.Z., Dong, C.Y., Wang, Q.: Adaptive control scheme for linear uncertain switched systems. In: AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii (2008)Google Scholar
  33. 33.
    Aouf, N., Boulet, B., Botez, R.: \({\cal{H}}_{2}\) and \({\cal{H}}_{\infty }\)-optimal gust load alleviation for a flexible aircraft. In: Proceeding of the American Control Conference, Chicago, Illinois, pp. 1872–1876 (2000)Google Scholar
  34. 34.
    Fang, M.: Synchronization for complex dynamical networks with time delay and discrete-time information. Appl. Math. Comput. 258(1), 1–11 (2015)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Que, H.Y., Fang, M., Wu, Z.-G., Su, H.Y., Huang, T.W., Zhang, D.: Exponential synchronization via aperiodic sampling of complex delayed networks. IEEE Trans. Syst. Man Cybern. Syst. (2018)
  36. 36.
    Zhao, D., Ding, S.X., Karimi, H.R., Li, Y.Y., Wang, Y.Q.: On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: a least squares method. Automatica 99, 203–212 (2019)MathSciNetGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of PhysicsLiaoning UniversityShenyangPeople’s Republic of China
  2. 2.Department of Electrical EngineeringYeungnam UniversityKyongsanRepublic of Korea
  3. 3.College of Information Science and EngineeringNortheastern UniversityShenyangPeople’s Republic of China

Personalised recommendations