Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 364726, 9 pages
http://dx.doi.org/10.1155/2013/364726
Research Article

Sliding Sector-Based Variable Structure Control of Continuous-Time Markov Jump Linear Systems Subject to Unknown Transition Rates

1The School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044, China
2The School of Automation, Southeast University, Nanjing, Jiangsu 210096, China

Received 8 August 2013; Accepted 5 October 2013

Academic Editor: Tao Li

Copyright © 2013 Yan-Mei Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Dai, D. Huang, and Z. Li, “Sliding mode control of hybrid joints for wheeled mobile manipulators with Markovian switching and bounded torques,” Intelligent Robotics and Applications, vol. 6424, no. 1, pp. 171–182, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. L. Ding, H. Gao, K. Xia, Z. Liu, J. Tao, and Y. Liu, “Adaptive sliding mode control of mobile manipulators with markovian switching joints,” Journal of Applied Mathematics, vol. 2012, Article ID 414315, 24 pages, 2012. View at Publisher · View at Google Scholar
  3. E. K. Boukas, Stochastic Switching Systems: Analysis and Design, Birkhauser, Berlin, Germany, 2005.
  4. E. K. Boukas and H. Yang, “Stability of discrete-time linear systems with Markovian jumping parameters,” Mathematics of Control, Signals, and Systems, vol. 8, no. 4, pp. 390–402, 1995. View at Publisher · View at Google Scholar · View at Scopus
  5. J. X. Dong and G.-H. Yang, “Robust H2 control of continuous-time Markov jump linear systems,” Automatica, vol. 44, no. 5, pp. 1431–1436, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. M. G. Todorov and M. D. Fragoso, “On the stability radii of continuous-time infinite Markov jump linear systems,” Mathematics of Control, Signals, and Systems, vol. 22, no. 1, pp. 23–38, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. O. L. V. Costa and E. K. Boukas, “Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps,” Journal of Optimization Theory and Applications, vol. 99, no. 2, pp. 359–379, 1998. View at Google Scholar · View at Scopus
  8. Z. Wang, J. Lam, and X. Liu, “Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances,” IEEE Transactions on Circuits and Systems II, vol. 51, no. 5, pp. 262–268, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Xu, T. Chen, and J. Lam, “Robust H filtering for uncertain Markovian jump systems with mode-dependent time delays,” IEEE Transactions on Automatic Control, vol. 48, no. 5, pp. 900–907, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Karan, P. Shi, and C. Y. Kaya, “Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems,” Automatica, vol. 42, no. 12, pp. 2159–2168, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. J. L. Xiong, J. Lam, H. J. Gao, and W. C. Daniel, “On robust stabilization of Markovian jump systems with uncertain switching probabilities,” Automatica, vol. 41, no. 5, pp. 897–903, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. L. Zhang, E.-K. Boukas, and J. Lam, “Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities,” IEEE Transactions on Automatic Control, vol. 53, no. 10, pp. 2458–2464, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. L. Zhang and E.-K. Boukas, “Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities,” Automatica, vol. 45, no. 2, pp. 463–468, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. L. Zhang and J. Lam, “Necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1695–1701, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. P. Y. Richard, H. Cormerais, and J. Buisson, “A generic design methodology for sliding mode control of switched systems,” Nonlinear Analysis: Theory, Methods and Applications, vol. 65, no. 9, pp. 1751–1772, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. G. S. Tombul, S. P. Banks, and N. Akturk, “Sliding mode control for a class of non-affine nonlinear systems,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, pp. 1589–1597, 2009. View at Google Scholar
  17. M. Roopaei and M. Z. Jahromi, “Chattering-free fuzzy sliding mode control in MIMO uncertain systems,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 10, pp. 4430–4437, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Niu, D. W. C. Ho, and J. Lam, “Robust integral sliding mode control for uncertain stochastic systems with time-varying delay,” Automatica, vol. 41, no. 5, pp. 873–880, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Niu, D. W. C. Ho, and X. Wang, “Sliding mode control for Itô stochastic systems with Markovian switching,” Automatica, vol. 43, no. 10, pp. 1784–1790, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. B. C. Zheng and G. H. Yang, “Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates,” International Journal of Systems Science, 2013. View at Publisher · View at Google Scholar
  21. P. Shi, Y. Xia, G. P. Liu, and D. Rees, “On designing of sliding-mode control for stochastic jump systems,” IEEE Transactions on Automatic Control, vol. 51, no. 1, pp. 97–103, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Ma and E.-K. Boukas, “A singular system approach to robust sliding mode control for uncertain Markov jump systems,” Automatica, vol. 45, no. 11, pp. 2707–2713, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applications, Taylor and Francis, London, UK, 1998.
  24. J. Y. Hung, W. B. Gao, and J. C. Hung, “Variable structure control: a survey,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 2–22, 1993. View at Publisher · View at Google Scholar · View at Scopus
  25. V. I. Utkin, Sliding Modes in Control and Optimization, Springer, Berlin, Germany, 1992.
  26. K. Furuta and Y. Pan, “Variable structure control with sliding sector,” Automatica, vol. 36, no. 2, pp. 211–228, 2000. View at Publisher · View at Google Scholar · View at Scopus
  27. I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems and Control Letters, vol. 8, no. 4, pp. 351–357, 1987. View at Google Scholar · View at Scopus
  28. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.