State Estimation and Reliable Control of Singular Markovian Systems with Distributed State Delays and Input Delays

  • Y. Y. Wang
  • P. F. Zhou
  • Q. B. Wang
  • D. P. Duan


This paper is concerned with state estimation and reliable control for singular Markovian jump systems with distributed state delays and input delays. Firstly, an observer is designed to estimate the system states, and a reliable controller is proposed based on the state estimates. Moreover, some conditions for the mean-square exponential admissibility of the overall closed-loop system are derived in terms of strict linear matrix inequality (LMI).


Singular Markovian jump systems Distributed delay Input delay Observer design Reliable control 



This work was supported by the National Hi-Tech Research and Development Program (863) of China (Grant No. 2011AA7052011).


  1. 1.
    Boukas, E.K.: Stochastic Hybrid Systems: Analysis and Design. Birkhauser, Boston (2005) Google Scholar
  2. 2.
    Chen, B., Niu, Y.G., Huang, H.Q.: Output feedback control for stochastic Markovian jumping systems via sliding mode design. Optim. Control Appl. Methods 32(1), 83–94 (2011) CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Gao, H.J., Fei, Z.Y., Lam, J., Du, B.Z.: Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays. IEEE Trans. Autom. Control 56(1), 223–229 (2011) CrossRefMathSciNetGoogle Scholar
  4. 4.
    Shi, P., Xia, Y., Liu, G.P., Rees, D.: On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51(1), 97–103 (2006) CrossRefMathSciNetGoogle Scholar
  5. 5.
    Shu, Z., Lam, J., Xu, S.: Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica 42(11), 2001–2008 (2006) CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Mahmoud, M.S.: Methodologies for Control of Jumping Time-Delay Systems. Kluwer Academic, Amsterdam (2003) Google Scholar
  7. 7.
    Mahmoud, M.S.: Delay-dependent dissipativity of singular time-delay systems. IMA J. Math. Control Inf. 26, 45–58 (2009) CrossRefMATHGoogle Scholar
  8. 8.
    Mahmoud, M.S., Emara-Shabaik, H.E.: New H 2 filter for uncertain singular systems using strict LMIs. Circuits Syst. Signal Process. 28, 665–677 (2009) CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Xu, S.Y., Lam, J.: Robust Control and Filtering of Singular Systems. Springer, Berlin (2006) MATHGoogle Scholar
  10. 10.
    Huang, L.R., Mao, X.R.: Stability of singular stochastic systems with Markovian switching. IEEE Trans. Autom. Control 56(2), 424–429 (2011) CrossRefMathSciNetGoogle Scholar
  11. 11.
    Wu, L.G., Daniel, H.W.C.: Sliding mode control of singular stochastic hybrid systems. Automatica 46(4), 779–783 (2010) CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Wu, L.G., Shi, P., Gao, H.J.: State estimation and sliding-mode control of Markovian jump singular systems. IEEE Trans. Autom. Control 55(5), 1213–1219 (2010) CrossRefMathSciNetGoogle Scholar
  13. 13.
    Xia, Y., Zhang, J., Boukas, E.K.: Control for discrete singular hybrid systems. Automatica 44(10), 2635–2641 (2008) CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Xia, Y., Boukas, E.K., Shi, P., Zhang, J.H.: Stability and stabilization of continuous-time singular hybrid systems. Automatica 45(6), 1504–1509 (2009) CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Boukas, E.K., Xu, S., Lam, J.: On stability and stabilizability of singular stochastic systems with delays. J. Optim. Theory Appl. 127(2), 249–262 (2005) CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Lam, J., Shu, Z., Xu, S., Boukas, E.K.: Robust H control of descriptor discrete-time Markovian jump systems. Int. J. Control 80(3), 374–385 (2007) CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Ma, S.P., Boukas, E.K.: Guaranteed cost control of uncertain discrete-time singular Markov jump systems with indefinite quadratic cost. Int. J. Robust Nonlinear Control 21(9), 1031–1045 (2011) CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Wu, Z.G., Su, H.Y., Chu, J.: Delay-dependent H control for singular Markovian jump systems with time-delay. Optim. Control Appl. Methods 30(5), 443–461 (2009) CrossRefMathSciNetGoogle Scholar
  19. 19.
    Wu, Z.G., Shi, P., Su, H.Y., Chu, J.: Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay. Int. J. Syst. Sci. 43(11), 2095–2106 (2012). doi: 10.1080/00207721.2011.564327 CrossRefMathSciNetGoogle Scholar
  20. 20.
    Cheng, C., Zhao, Q.: Reliable control of uncertain delayed systems with integral quadratic constraints. IEE Proc., Control Theory Appl. 151(6), 790–796 (2004) CrossRefGoogle Scholar
  21. 21.
    Al-Rayyah, A.Y., Mahmoud, M.S.: Decentralized reliable control of interconnected time-delay systems against sensor failures. J. Optim. Theory Appl. 147, 318–336 (2010) CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Liang, Y.W., Xu, S.D.: Reliable control of nonlinear systems via variable structure scheme. IEEE Trans. Autom. Control 51(10), 1721–1726 (2006) CrossRefMathSciNetGoogle Scholar
  23. 23.
    Mahmoud, M.S.: Decentralized reliable control of interconnected systems with time-varying delays. J. Optim. Theory Appl. 143, 497–518 (2009) CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Mahmoud, M.S.: Resilient decentralized stabilization for interconnected discrete-time systems. J. Optim. Theory Appl. 145, 507–525 (2010) CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Yang, G.H., Wang, J.L., Soh, Y.C.: Reliable H controller design for linear systems. Automatica 37(5), 717–725 (2001) CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Zhang, H., Guan, Z.H., Feng, G.: Reliable dissipative control for stochastic impulse systems. Automatica 44(4), 1004–1010 (2008) CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Yue, D., Han, Q.L.: Robust H filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Trans. Signal Process. 52(11), 3200–3212 (2004) CrossRefMathSciNetGoogle Scholar
  28. 28.
    Petersen, I.R.: A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8(4), 351–357 (1987) CrossRefMATHGoogle Scholar
  29. 29.
    Gu, K., Kharitonov, V.K., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Boston (2003) CrossRefMATHGoogle Scholar
  30. 30.
    Mao, X., Koroleva, N., Rodikin, A.: Robust stability of uncertain stochastic differential delay equations. Syst. Control Lett. 35(5), 325–336 (1998) CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Y. Y. Wang
    • 1
  • P. F. Zhou
    • 1
  • Q. B. Wang
    • 1
  • D. P. Duan
    • 1
  1. 1.School of Aeronautics and AstronauticsShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations