Robust Control for Markov Jump Systems

  • Hongjiu Yang
  • Yuanqing Xia
  • Qing Geng
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 193)


It is known that Markov jump systems have finite modes which may jump from one to another at different times and between different modes. A system with “jumping” character may be modeled as a hybrid system, and the parameter jumps among different modes can be seen as discrete events [119]. Until now, only a little results on Markov jump DOSs have been obtained. Stability analysis of Markov jump DOSs over networks has been given in [167]. By letting each intermittent interval satisfy the corresponding Markov jump process, a class of DOSs has been used to describe NCSs in [169]. A problem on robust stabilization has been concerned of singular Markov jump systems with time-varying delays and parameter uncertainties [208]. There are also several results along a line of actuator saturation for the Markov jump systems.


  1. 78.
    H. Liu, F. Sun, E.-K. Boukas, D. Ho, Controller design for Markov jumping systems subject to actuator saturation. Automatica 42(3), 459–465 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 79.
    H. Liu, F. Sun, E. Boukas, Robust control of uncertain discrete-time Markovian jump systems with actuator saturation. Int. J. Control 79(7), 805–812 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 94.
    S. Ma, C. Zhang, S. Zhu, Robust stability for discrete-time uncertain singular Markov jump systems with actuator saturation. IET Control Theory Appl. 5(2), 255–262 (2011)MathSciNetCrossRefGoogle Scholar
  4. 119.
    P. Shi, Y. Xia, G.-P. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51(1), 97–103 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 139.
    Y. Wang, C. Wang, Z. Zuo, Controller synthesis for Markovian jump systems with incomplete knowledge of transition probabilities and actuator saturation. J. Frankl. Inst. 348(9), 2417–2429 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 167.
    H. Yang, Y. Xia, P. Shi, M. Fu, Stability analysis for high frequency networked control systems. IEEE Trans. Autom. Control 57(10), 2694–2700 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 169.
    H. Yang, Y. Xia, P. Shi, B. Liu, Guaranteed cost control of networked control systems based on delta operator Kalman filter. Int. J. Adapt. Control Signal Process. 27(8), 701–717 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 170.
    H. Yang, Y. Xia, P. Shi, L. Zhao, Analysis and Synthesis of Delta Operator Systems (Springer, Berlin/Heidelberg, 2012)CrossRefGoogle Scholar
  9. 208.
    G. Zhuang, J. Xia, B. Zhang, W. Sun, Robust normalisation and PCD state feedback control for uncertain singular Markovian jump systems with time-varying delays. IET Control Theory Appl. 12(3), 419–427 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Hongjiu Yang
    • 1
  • Yuanqing Xia
    • 2
  • Qing Geng
    • 3
  1. 1.School of Electrical and Information EngineeringTianjin UniversityTianjinChina
  2. 2.School of AutomationBeijing Institute of TechnologyBeijingChina
  3. 3.Institute of Electrical EngineeringYanshan UniversityQinhuangdaoChina

Personalised recommendations