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Mathematical Problems in Engineering
Volume 2013, Article ID 197819, 8 pages
http://dx.doi.org/10.1155/2013/197819
Research Article

Robust Reliable Control of Uncertain Discrete Impulsive Switched Systems with State Delays

1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 10 December 2012; Revised 5 January 2013; Accepted 19 January 2013

Academic Editor: Ligang Wu

Copyright © 2013 Xia 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. D. Liberzon, Switching in Systems and Control, Birkhäuser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59–70, 1999. View at Publisher · View at Google Scholar · View at Scopus
  3. J. P. Hespanha and A. S. Morse, “Stability of switched systems with average dwell-time,” in Proceedings of the 38th IEEE Conference on Decision and Control (CDC '99), vol. 3, pp. 2655–2660, December 1999. View at Scopus
  4. J. C. Geromel and P. Colaneri, “H and dwell time specifications of switched linear systems,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08, pp. 5318–5323, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. D.-W. Ding and G.-H. Yang, “H static output feedback control for discrete-time switched linear systems with average dwell time,” IET Control Theory & Applications, vol. 4, no. 3, pp. 381–390, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. L. Wu, T. Qi, and Z. Feng, “Average dwell time approach to L2L control of switched delay systems via dynamic output feedback,” IET Control Theory & Applications, vol. 3, no. 10, pp. 1425–1436, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  7. W.-A. Zhang and L. Yu, “Stability analysis for discrete-time switched time-delay systems,” Automatica, vol. 45, no. 10, pp. 2265–2271, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. Zhang and B. Jiang, “Stability of a class of switched linear systems with uncertainties and average dwell time switching,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 2, pp. 667–676, 2010. View at Google Scholar · View at Scopus
  9. P. Yan and H. Ozbay, “Stability analysis of switched time delay systems,” SIAM Journal on Control and Optimization, vol. 47, no. 2, pp. 936–949, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Wu, D. W. C. Ho, and C. W. Li, “Sliding mode control of switched hybrid systems with stochastic perturbation,” Systems & Control Letters, vol. 60, no. 8, pp. 531–539, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L. Wu, D. W. C. Ho, and C. W. Li, “Stabilisation and performance synthesis for switched stochastic systems,” IET Control Theory & Applications, vol. 4, no. 10, pp. 1877–1888, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Z.-H. Guan, D. J. Hill, and X. Shen, “On hybrid impulsive and switching systems and application to nonlinear control,” IEEE Transactions on Automatic Control, vol. 50, no. 7, pp. 1058–1062, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  13. B. Liu and H. J. Marquez, “Controllability and observability for a class of controlled switching impulsive systems,” IEEE Transactions on Automatic Control, vol. 53, no. 10, pp. 2360–2366, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Ye, A. N. Michel, and L. Hou, “Stability analysis of systems with impulse effects,” IEEE Transactions on Automatic Control, vol. 43, no. 12, pp. 1719–1723, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Z. G. Li, C. Y. Wen, and Y. C. Soh, “Analysis and design of impulsive control systems,” IEEE Transactions on Automatic Control, vol. 46, no. 6, pp. 894–897, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. H. Lee and J. T. Lim, “Stability analysis of switched systems with impulse effects,” in Proceedings of the IEEE International Symposium on Intelligent Control-Intelligent Systems and Semiotics, pp. 79–83, Cambridge, Mass, USA, September 1999. View at Scopus
  17. S. Cong, Y. Zou, and Y. Zhang, “Stability and output feedback stabilization for systems with Markovian switching and impulse effects,” Journal of Control Theory and Applications, vol. 8, no. 4, pp. 453–456, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  18. L. Wu and W. X. Zheng, “Passivity-based sliding mode control of uncertain singular time-delay systems,” Automatica, vol. 45, no. 9, pp. 2120–2127, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems,” Automatica, vol. 48, no. 8, pp. 1929–1933, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. J. Wu, X. Chen, and H. Gao, “H filtering with stochastic sampling,” Signal Processing, vol. 90, no. 4, pp. 1131–1145, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. L. Wu and W. X. Zheng, “Weighted H model reduction for linear switched systems with time-varying delay,” Automatica, vol. 45, no. 1, pp. 186–193, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. L. Wu, Z. Feng, and W. X. Zheng, “Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach,” IEEE Transactions on Neural Networks, vol. 21, no. 9, pp. 1396–1407, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. G. Zong, S. Xu, and Y. Wu, “Robust H stabilization for uncertain switched impulsive control systems with state delay: an LMI approach,” Nonlinear Analysis. Hybrid Systems. An International Multidisciplinary Journal, vol. 2, no. 4, pp. 1287–1300, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. H. Xu, X. Liu, and K. L. Teo, “A LMI approach to stability analysis and synthesis of impulsive switched systems with time delays,” Nonlinear Analysis. Hybrid Systems. An International Multidisciplinary Journal, vol. 2, no. 1, pp. 38–50, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. W. Zhu, “Stability analysis of switched impulsive systems with time delays,” Nonlinear Analysis. Hybrid Systems. An International Multidisciplinary Journal, vol. 4, no. 3, pp. 608–617, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Y. Liu and W. Feng, “Razumikhin-Lyapunov functional method for the stability of impulsive switched systems with time delay,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 249–264, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. Z. Xiang and R. Wang, “Robust L reliable control for uncertain nonlinear switched systems with time delay,” Applied Mathematics and Computation, vol. 210, no. 1, pp. 202–210, 2009. View at Publisher · View at Google Scholar · View at Scopus
  28. Z. Xiang, Y.-N. Sun, and Q. Chen, “Robust reliable stabilization of uncertain switched neutral systems with delayed switching,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9835–9844, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. R. Wang, M. Liu, and J. Zhao, “Reliable H control for a class of switched nonlinear systems with actuator failures,” Nonlinear Analysis. Hybrid Systems. An International Multidisciplinary Journal, vol. 1, no. 3, pp. 317–325, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. D. Zhang and L. Yu, “Fault-tolerant control for discrete-time switched linear systems with time-varying delay and actuator saturation,” Journal of Optimization Theory and Applications, vol. 153, no. 1, pp. 157–176, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. H. Yang, B. Jiang, and V. Cocquempot, “Observer-based fault-tolerant control for a class of hybrid impulsive systems,” International Journal of Robust and Nonlinear Control, vol. 20, no. 4, pp. 448–459, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  32. C. Liu and Z. R. Xiang, “Robust L reliable control for impulsive switched nonlinear systems with state delay,” Journal of Applied Mathematics and Computing, 2012. View at Publisher · View at Google Scholar
  33. H. Yang, B. Jiang, and V. Cocquempot, “Fault tolerant control for a class of hybrid impulsive systems,” in Proceedings of the American Control Conference (ACC '08), pp. 3287–3292, Seattle, Wash, USA, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Mahmoudi, A. Momeni, A. G. Aghdam, and P. Gohari, “On observer design for a class of impulsive switched systems,” in Proceedings of the American Control Conference (ACC '08), pp. 4633–4639, Seattle, Wash, USA, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  35. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  36. L. Xie, “Output feedback H control of systems with parameter uncertainty,” International Journal of Control, vol. 63, no. 4, pp. 741–750, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  37. I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems & Control Letters, vol. 8, no. 4, pp. 351–357, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. Y. Zhang, C. Liu, and H. Sun, “Robust finite-time H control for uncertain discrete jump systems with time delay,” Applied Mathematics and Computation, vol. 219, no. 5, pp. 2465–2477, 2012. View at Publisher · View at Google Scholar · View at MathSciNet