Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 545636, 16 pages
http://dx.doi.org/10.1155/2013/545636
Research Article

Delay-Dependent Control for Descriptor Markovian Jump Systems with Time-Varying Delay

1Institute of Systems Science, Northeastern University, Shenyang 110819, China
2School of Science, Shenyang University of Technology, Shenyang 110870, China

Received 11 August 2013; Accepted 20 September 2013

Academic Editor: Baolin Wang

Copyright © 2013 Jinghao Li 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. K. Gu, V. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhauser, Boston, Mass, USA, 2003.
  2. E. Fridman, “New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems,” Systems & Control Letters, vol. 43, no. 4, pp. 309–319, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Q.-L. Han, “Robust stability of uncertain delay-differential systems of neutral type,” Automatica, vol. 38, no. 4, pp. 719–723, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. He, M. Wu, J.-H. She, and G.-P. Liu, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays,” Systems & Control Letters, vol. 51, no. 1, pp. 57–65, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X.-G. Li, X.-J. Zhu, A. Cela, and A. Reama, “Stability analysis of neutral systems with mixed delays,” Automatica, vol. 44, no. 11, pp. 2968–2972, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X.-L. Zhu and G.-H. Yang, “New results of stability analysis for systems with time-varying delay,” International Journal of Robust and Nonlinear Control, vol. 20, no. 5, pp. 596–606, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. Shao, “New delay-dependent stability criteria for systems with interval delay,” Automatica, vol. 45, no. 3, pp. 744–749, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica, vol. 47, no. 1, pp. 235–238, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E.-K. Boukas, Control of Singular Systems with Random Abrupt Changes, Springer, Berlin, Germany, 2008. View at MathSciNet
  10. S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, vol. 332 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2006. View at MathSciNet
  11. Z. Fei, H. Gao, and P. Shi, “New results on stabilization of Markovian jump systems with time delay,” Automatica, vol. 45, no. 10, pp. 2300–2306, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Xu, J. Lam, and X. Mao, “Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays,” IEEE Transactions on Circuits and Systems I, vol. 54, no. 9, pp. 2070–2077, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. H. Huang, G. Feng, and X. Chen, “Stability and stabilization of Markovian jump systems with time delay via new Lyapunov functionals,” IEEE Transactions on Circuits and Systems I, vol. 59, no. 10, pp. 2413–2421, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Yu, W. Sun, and H. Liu, “Improved H analysis of Markovian jumping stochastic systems with time-varying delays,” International Journal of Systems Science, vol. 44, no. 3, pp. 521–532, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. L. Dai, Singular Control Systems, vol. 118 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Z.-G. Wu, J. H. Park, H. Su, and J. Chu, “Delay-dependent passivity for singular Markov jump systems with time-delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 3, pp. 669–681, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. J. Wang, H. Wang, A. Xue, and R. Lu, “Delay-dependent H control for singular Markovian jump systems with time delay,” Nonlinear Analysis. Hybrid Systems, vol. 8, pp. 1–12, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. K. Gu, “An integral inequality in the stability problem of time-delay systems,” in Proceedings of the 39th IEEE Confernce on Decision and Control, pp. 2805–2810, Sydney, Australia, December 2000. View at Scopus
  19. E. Uezato and M. Ikeda, “Strict LMI conditions for stability, robust stabilization, and H control of descriptor systems,” in Proceedings of the The 38th IEEE Conference on Decision and Control (CDC '99), pp. 4092–4097, December 1999. View at Scopus
  20. Z. Wu, H. Su, and J. Chu, “Delay-dependent stabilization of singular Markovian jump systems with state delay,” Journal of Control Theory and Applications, vol. 7, no. 3, pp. 231–236, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet