Delay-dependent H control for jumping delayed systems with two Markov processes

  • Hao Shen
  • Yuming Chu
  • Shengyuan Xu
  • Zhengqiang Zhang
Regular Papers Control Theory


This paper addresses the H control problem for jumping delayed systems with two separable Markov processes. The objective is to design a controller such that the resulting closed-loop system is exponentially mean-square stable with a given decay rate and satisfies a prescribed H performance level. A decay-rate-dependent condition is obtained for the existence of admissible controllers in term of linear matrix inequalities. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.


Exponential stability H control jumping delayed systems Markov processes 


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  1. [1]
    J. Dong and G. Yang, “Fuzzy controller design for Markovian jump nonlinear systems,” Int. J. Control, Automation, and Systems, vol. 5, pp. 712–717, 2007.Google Scholar
  2. [2]
    H. Shen, S. Xu, X. Song, and J. Luo, “Delay-dependent robust stabilization for uncertain stochastic switching systems with distributed delays,” Asian Journal of Control, vol. 11, pp. 527–535, 2009.MathSciNetCrossRefGoogle Scholar
  3. [3]
    P. Shi, Y. Xia, G. Liu, and D. Rees, “On designing of sliding mode control for stochastic jump systems,” IEEE Trans. Automat. Control, vol. 51, pp. 97–103, 2006.MathSciNetCrossRefGoogle Scholar
  4. [4]
    S. Xu, T. Chen, and J. Lam, “Robust H filtering for uncertain Markovian jump systems with mode dependent time delays,” IEEE Trans. Automat. Control, vol. 48, pp. 900–907, 2003.MathSciNetCrossRefGoogle Scholar
  5. [5]
    P. Shi, E. K. Boukas, S. Nguang, and X. Guo, “Robust disturbance attenuation for discrete-time active fault tolerant systems with uncertainties,” Optim. Control Appl. Methods, vol. 24, pp. 85–101, 2003.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    L. Hu, P. Shi, and B. Huang, “H control for sampled data linear systems with two Markov processes,” Optim. Control Appl. Methods, vol. 26, pp. 291–306, 2005.MathSciNetCrossRefGoogle Scholar
  7. [7]
    P. G. Park and J. Wan Ko, “Stability and robust stability for systems with a time-varying delay,” Automatica, vol. 43, pp. 1855–1858, 2007.MATHCrossRefGoogle Scholar
  8. [8]
    Y. Zhang and E. Tian, “Novel robust delay-dependent exponential stability criteria for stochas tic delayed recurrent neural networks,” Int. J. Innovative Computing, Information and Control, vol. 5, pp. 2735–2744, 2009.Google Scholar
  9. [9]
    S. Mondié and V. L. Kharitonov, “Exponential estimates for retarded time-delay systems: an LMI approach,” IEEE Trans. Automat. Control, vol. 50, pp. 268–273, 2005.MathSciNetCrossRefGoogle Scholar
  10. [10]
    S. Xu, J. Lam, and M. Zhong, “New exponential estimates for time-delay systems,” IEEE Trans. Automat. Control, vol. 51, pp. 1501–1505, 2006.MathSciNetCrossRefGoogle Scholar
  11. [11]
    B. Zhang, J. Lam, S. Xu, and Z. Shu, “Robust stabilization of uncertain T-S fuzzy time-delay systems with exponential estimates,” Fuzzy Sets and Systems, vol. 160, pp. 1720–1737, 2009.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Z. Shu, J. Lam, and S. Xu, “Robust stabilization of Markovian delay systems with delay-dependent exponential estimates,” Automatica, vol. 42, pp. 2001–2008, 2006.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    P. Apkarian, H. D. Tuan, and J. Bernussou, “Continuous-time analysis, eigenstructure assignment, and H 2 synthesis with enhanced linear matrix inequalities (LMI) characterizations,” IEEE Trans. Automat. Control, vol. 46, pp. 1941–1946, 2001.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    L. Hu, P. Shi, and Y. Cao, “Delay-dependent filtering design for time-delay systems with Markovian jumping parameters,” Int. J. Adapt. Control Signal Process, vol. 21, pp. 434–448, 2007.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    J. Wu, T. Chen, and L. Wang, “Delay-dependent robust stability and H control for jump linear systems with delays,” Systems & Control Lett., vol. 55, pp. 939–948, 2006.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    Z. Wu, H. Su, and J. Chu, “Delay-dependent H control for singular Markovian jump systems with time delay,” Optim. Control Appl. Methods, vol. 30, pp. 443–461, 2009.MathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hao Shen
    • 1
    • 2
  • Yuming Chu
    • 3
  • Shengyuan Xu
    • 1
  • Zhengqiang Zhang
    • 1
  1. 1.School of AutomationNanjing University of Science and TechnologyNanjingChina
  2. 2.School of Electrical Engineering & InformationAnhui University of TechnologyMa’anshanChina
  3. 3.School of ScienceHuzhou Teachers CollegeHuzhouChina

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