Stabilization for Markov Jump Delay Systems

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


Markov jump systems are a kind of multimode systems which have been studied in lots of literatures [66, 206]. However, it is difficult to obtain complete known transition probabilities in practice even impossible. Therefore, analysis on Markov jump systems with incomplete transition descriptions is an interesting problem. A robust controller has been designed for a kind of Markov jump DOSs with actuator saturation in [160]. An adaptive sliding mode controller has been designed for spacecraft systems with actuator saturation [207]. An exponential stability condition has been derived for time-delay systems using a weighted integral inequality approach in [37]. Due to promotion of above results, analysis of systems with time-varying delays and actuator saturation has attracted widely attentions.


  1. 37.
    C. Gong, G. Zhu, L. Wu, New weighted integral inequalities and its application to exponential stability analysis of time-delay systems. IEEE Access 4(99), 6231–6237 (2016)CrossRefGoogle Scholar
  2. 39.
    Z. Gu, D. Yue, C. Peng, J. Liu, J. Zhang, Fault tolerant control for systems with interval time-varying delay and actuator saturation. J. Frankl. Inst. 350(2), 231–243 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 66.
    H. Li, P. Shi, D. Yao, L. Wu, Observer-based adaptive sliding mode control for nonlinear Markovian jump systems. Automatica 64, 133–142 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 91.
    J. Lu, Y. Xi, D. Li, Y. Xu, Z. Gan, Model predictive control synthesis for constrained Markovian jump linear systems with bounded disturbance. IET Control Theory Appl. 11(18), 3288–3296 (2018)MathSciNetCrossRefGoogle Scholar
  5. 160.
    H. Yang, H. Li, F. Sun, Y. Yuan, Robust control for Markovian jump delta operator systems with actuator saturation. Eur. J. Control 20(4), 207–215 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 188.
    L. Zhang, E. Boukas, A. Haidar, Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Automatica 44(10), 2691–2695 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 206.
    J. Zhu, L. Wang, M. Spiryagin, Control and decision strategy for a class of Markovian jump systems in failure prone manufacturing process. IET Control Theory Appl. 6(12), 1803–1811 (2012)MathSciNetCrossRefGoogle Scholar
  8. 207.
    Z. Zhu, Y. Xia, M. Fu, Adaptive sliding mode control for attitude stabilization with actuator saturation. IEEE Trans. Ind. Electron. 58(10), 4898–4907 (2011)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