Decentralized Observer-Based Reliable Control for a Class of Interconnected Markov Jumped Time-Delay System Subject to Actuator Saturation and Failure

  • Zhaohui Chen
  • Zhong Cao
  • Qi Huang
  • Stephen L. Campbell


A decentralized stabilization method is investigated for a class of interconnected Markov jumping systems subject to time-varying delays, actuator saturation and jumped failure. The mean-square exponential stability condition is established by constructing multiple Lyapunov–Krasovskii functionals, which are delay-dependent, mode-dependent and decay rate-dependent. Taking into account the influence of actuator saturation and jumped actuator failure, decentralized observer-based \( H_{\infty } \) state feedback stabilization schemes are designed. The decentralized observer gains and controller gains are determined by solving a convex optimization problem with \( H_{\infty } \) performance \( \gamma^{2} \) as objective and LMIs as constraints. Simulation results are also presented to illustrate the effectiveness and applicability of the obtained results.


Interconnected systems Time-delay systems Actuator saturation Actuator failure Decentralized observer-based stabilization 



This work was supported by the National Natural Science Foundation of China under Grant No. 51277022, Chongqing Education Council Foundation under Grant Nos. KJ1501312 and KJ1601310, Chongqing University of Science and Technology doctoral Foundation under Grant No. CK2016B17, and China Scholarship Council under Grant No. 201608505169.


  1. 1.
    S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (Siam, Philadelphia, 1994)CrossRefzbMATHGoogle Scholar
  2. 2.
    R. Chang, Y. Fang, L. Liu, J. Li, Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation. Int. J. Adapt. Control 31(2), 255–274 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Y. Ding, H. Liu, Stability analysis of continuous-time Markovian jump time-delay systems with time-varying transition rates. J. Frankl. Inst. 353(11), 2418–2430 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    C.X. Dou, Z.S. Duan, X.B. Jia, Delay-dependent H robust control for large power systems based on two-level hierarchical decentralised coordinated control structure. Int. J. Syst. Sci. 44(2), 329–345 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    J.H. Fan, Y.M. Zhang, Z.Q. Zheng, Robust fault-tolerant control against time-varying actuator faults and saturation. IET Control Theory A 6(14), 2198–2208 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Y.M. Fu, C.J. Li, Parametric method for spacecraft trajectory tracking control problem with stochastic thruster fault. IET Control Theory A 10(17), 2331–2338 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    S. Ghosh, S.K. Das, G. Ray, Stability analysis of interconnected time-delay systems in a generalised framework. IET Control Theory A 4(12), 3022–3032 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems (Birkhäuser, Boston, 2003)CrossRefzbMATHGoogle Scholar
  9. 9.
    Z. Gu, J. Liu, C. Peng, E. Tian, Reliable control for interval time-varying delay systems subjected to actuator saturation and stochastic failure. Optim. Control Appl. Methods 33(6), 739–750 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Z. Gu, D. Yue, D. Wang, J. Liu, Stochastic faulty actuator-based reliable control for a class of interval time-varying delay systems with Markovian jumping parameters. Optim. Control Appl. Methods 32(3), 313–327 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    D.W. Ho, G. Lu, Robust stabilization for a class of discrete-time non-linear systems via output feedback: the unified LMI approach. Int. J. Control 76(2), 105–115 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Z. Hou, J. Luo, P. Shi, S.K. Nguang, Stochastic stability of Ito differential equations with semi-Markovian jump parameters. IEEE Trans. Autom. Control 51(8), 1383–1387 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    T. Hu, Z. Lin, B.M. Chen, An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38(2), 351–359 (2002)CrossRefzbMATHGoogle Scholar
  14. 14.
    Z. Hu, Decentralized stabilization of large scale interconnected systems with delays. IEEE Trans. Autom. Control 39(1), 180–182 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    C.C. Hua, Q.G. Wang, X.P. Guan, Exponential stabilization controller design for interconnected time delay systems. Automatica 44(10), 2600–2606 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    J. Huang, Y. Shi, X. Zhang, Active fault tolerant control systems by the semi-Markov model approach. Int. J. Adapt. Control 28(9), 833–847 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    X.Z. Jin, Y.G. He, Y.G. He, Finite-time robust fault-tolerant control against actuator faults and saturations. IET Control Theory A 11(4), 550–556 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    G.P. Kladis, Stabilisation and tracking for swarm-based UAV missions subject to time-delay. in Applications of Mathematics and Informatics in Science and Engineering, ed. by N.J. Daras (Springer, Cham, 2014), pp. 265–288CrossRefGoogle Scholar
  19. 19.
    G.B. Koo, J.B. Park, Y.H. Joo, Decentralized fuzzy observer-based output-feedback control for nonlinear large-scale systems: an LMI approach. IEEE Trans. Fuzzy Syst. 22(2), 406–419 (2014)CrossRefGoogle Scholar
  20. 20.
    F. Li, C. Du, C. Yang, W. Gui, Passivity-based asynchronous sliding mode control for delayed singular Markovian jump systems. IEEE Trans. Autom. Control (2017). Google Scholar
  21. 21.
    F. Li, P. Shi, C.C. Lim, L. Wu, Fault detection filtering for nonhomogeneous Markovian jump systems via fuzzy approach. IEEE Trans. Fuzzy Syst. (2016). Google Scholar
  22. 22.
    F. Li, L. Wu, P. Shi, Stochastic stability of semi-Markovian jump systems with mode-dependent delays. Int. J. Robust Nonlinear 24(18), 3317–3330 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    F. Li, L. Wu, P. Shi, C.C. Lim, State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Automatica 51, 385–393 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    L.W. Li, G.H. Yang, Decentralized fault detection and isolation of Markovian jump interconnected systems with unknown interconnections. Int. J. Robust Nonlinear 27(16), 3321–3349 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    L. Li, V.A. Ugrinovskii, R. Orsi, Decentralized robust control of uncertain Markov jump parameter systems via output feedback. Automatica 43(11), 1932–1944 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Y. Li, S. Fei, B. Zhang, Y. Chu, Decentralized L2-L filtering for interconnected Markovian jump systems with delays. Circuits Syst. Signal Process. 31(3), 889–909 (2012)CrossRefzbMATHGoogle Scholar
  27. 27.
    Z. Lin, J. Liu, W. Zhang, Y. Niu, Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach. Automatica 47(12), 2796–2800 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    S. Ma, J. Xiong, V.A. Ugrinovskii, I.R. Petersen, Robust decentralized stabilization of Markovian jump large-scale systems: a neighboring mode dependent control approach. Automatica 49(10), 3105–3111 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Y. Ma, P. Yang, Y. Yan, Q. Zhang, Robust observer-based passive control for uncertain singular time-delay systems subject to actuator saturation. ISA Trans. 67, 9–18 (2017)CrossRefGoogle Scholar
  30. 30.
    M.S. Mahmoud, Decentralized reliable control of interconnected systems with time-varying delays. J. Optim. Theory Appl. 143(3), 497–518 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    M.S. Mahmoud, Interconnected jumping time-delay systems: mode-dependent decentralized stability and stabilization. Int. J. Robust Nonlinear 22(7), 808–826 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    M.S. Mahmoud, N.B. Almutairi, Resilient decentralized stabilization of interconnected time-delay systems with polytopic uncertainties. Int. J. Robust Nonlinear 21(4), 355–372 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    M.S. Mahmoud, Y. Xia, A generalized approach to stabilization of linear interconnected time-delay systems. Asian J. Control 14(6), 1539–1552 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    P. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235–238 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    W. Qi, X. Gao, H observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation. Appl. Math. Comput. 289, 80–97 (2016)MathSciNetGoogle Scholar
  36. 36.
    W. Qi, X. Gao, Y. Kao, L. Lian, J. Wang, Stabilization for positive Markovian jump systems with actuator saturation. Circuits Syst. Signal Process. 36(1), 374–388 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    M. Rehan, N. Iqbal, K.S. Hong, Delay-range-dependent control of nonlinear time-delay systems under input saturation. Int. J. Robust Nonlinear 26(8), 1647–1666 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    P. Shi, F. Li, L. Wu, C.C. Lim, Neural network-based passive filtering for delayed neutral-type semi-Markovian jump systems. IEEE Trans. Neural. Netw. Learn. 28(9), 2101–2114 (2017)MathSciNetGoogle Scholar
  39. 39.
    S.B. Stojanovic, D.D. Lj, Delay-dependent stability of linear discrete large scale time delay systems: necessary and sufficient conditions. Int. J. Syst. Sci. 4(2), 241–250 (2008)MathSciNetzbMATHGoogle Scholar
  40. 40.
    A.S. Tlili, Linear matrix inequality robust tracking control conditions for nonlinear disturbed interconnected systems. J. Dyn. Syst. T. ASME 139(6), 061002 (2017)CrossRefGoogle Scholar
  41. 41.
    A.S. Tlili, N.B. Braiek, Systematic linear matrix inequality conditions to design a robust decentralised observer-based optimal control for interconnected systems. IET Control Theory A 6(18), 2737–2747 (2012)MathSciNetCrossRefGoogle Scholar
  42. 42.
    V. Ugrinovskii, H.R. Pota, Decentralized control of power systems via robust control of uncertain Markov jump parameter systems. Int. J. Control 78(9), 662–677 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    C. Wang, C. Wen, L. Guo, Decentralized output-feedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures. Automatica 71, 187–196 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Z. Wang, Y. Liu, X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656–1662 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Z. Wang, Y. Liu, X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656–1662 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    F. Wu, Z. Lin, Q. Zheng, Output feedback stabilization of linear systems with actuator saturation. IEEE Trans. Autom. Control 52(1), 122–128 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    T. Wu, F. Li, C. Yang, W. Gui, Event-based fault detection filtering for complex networked jump systems. IEEE/ASME Trans. Mechatron. (2017). Google Scholar
  48. 48.
    S. Xie, L. Xie, Stabilization of a class of uncertain large-scale stochastic systems with time delays. Automatica 36(1), 161–167 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    S. Xu, J. Lam, X. Mao, Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits I 54(9), 2070–2077 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    X.G. Yan, S.K. Spurgeon, C. Edwards, Global decentralised static output feedback sliding-mode control for interconnected time-delay systems. IET Control Theory A 6(2), 192–202 (2012)MathSciNetCrossRefGoogle Scholar
  51. 51.
    X.G. Yan, S.K. Spurgeon, C. Edwards, Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback. Automatica 49(2), 633–641 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    T. Yang, L. Zhang, X. Yin, Time-varying gain-scheduling σ-error mean square stabilisation of semi-Markov jump linear systems. IET Control Theory A 10(11), 1215–1223 (2016)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Y. Yang, D. Yue, Y. Xue, Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation. J. Frankl. Inst. 352(5), 2129–2151 (2015)MathSciNetCrossRefGoogle Scholar
  54. 54.
    L. Zhang, E.K. Boukas, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(2), 463–468 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    L. Zhang, T. Yang, P. Colaneri, Stability and stabilization of semi-Markov jump linear systems with exponentially modulated periodic distributions of sojourn time. IEEE Trans. Autom. Control 62(6), 2870–2885 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsChongqing University of Science and TechnologyChongqingChina
  2. 2.School of Physics and Electronic EngineeringGuangzhou UniversityGuangzhouChina
  3. 3.Sichuan Provincial Key Lab of Power System Wide-Area Measurement and ControlUniversity of Electronic Science and Technology of ChinaChengduChina
  4. 4.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Personalised recommendations