About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 630545, 5 pages
http://dx.doi.org/10.1155/2013/630545
Research Article

Stabilization Analysis for the Switched Large-Scale Discrete-Time Systems via the State-Driven Switching

Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan

Received 15 February 2013; Accepted 7 April 2013

Academic Editor: Her-Terng Yau

Copyright © 2013 Chi-Jo Wang and Juing-Shian Chiou. 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 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
  2. A. S. Morse, “Supervisory control of families of linear set-point controllers. I. Exact matching,” IEEE Transactions on Automatic Control, vol. 41, no. 10, pp. 1413–1431, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. Frasca, L. Iannelli, and F. Vasca, “Dithered sliding-mode control for switched systems,” IEEE Transactions on Circuits and Systems II, vol. 53, no. 9, pp. 872–876, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Zhai, D. Liu, J. Imae, and T. Kobayashi, “Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems,” IEEE Transactions on Circuits and Systems II, vol. 53, no. 2, pp. 152–156, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. T.-H. Kim, S.-H. Lee, and J.-T. Lim, “Stability analysis of switched systems via redundancy factors,” International Journal of Systems Science, vol. 32, no. 10, pp. 1199–1204, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X. Zhang, Z. Q. Xia, and Y. Gao, “Exponential stabilizability of switched systems with polytopic uncertainties,” Journal of Applied Mathematics, vol. 2012, Article ID 853170, 15 pages, 2012. View at Publisher · View at Google Scholar
  7. B. Du and X. Zhang, “Delay-dependent stability analysis and synthesis for uncertain impulsive switched system with mixed delays,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 381571, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Ji, L. Wang, and G. Xie, “Quadratic stabilization of switched systems,” International Journal of Systems Science, vol. 36, no. 7, pp. 395–404, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D. Cheng, L. Guo, and J. Huang, “On quadratic Lyapunov functions,” IEEE Transactions on Automatic Control, vol. 48, no. 5, pp. 885–890, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Yang, X. Zhengrong, C. Qingwei, and H. Weili, “Robust reliable control of switched uncertain systems with time-varying delay,” International Journal of Systems Science, vol. 37, no. 15, pp. 1077–1087, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z. G. Li, C. Y. Wen, and Y. C. Soh, “Stabilization of a class of switched systems via designing switching laws,” IEEE Transactions on Automatic Control, vol. 46, no. 4, pp. 665–670, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Z. Sun and S. S. Ge, “Analysis and synthesis of switched linear control systems,” Automatica, vol. 41, no. 2, pp. 181–195, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. Ji, L. Wang, G. Xie, and F. Hao, “Linear matrix inequality approach to quadratic stabilisation of switched systems,” IEE Proceedings, vol. 151, no. 3, pp. 289–294, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. 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), pp. 2655–2660, December 1999. View at Scopus
  15. G. Zhai, B. Hu, K. Yasuda, and A. N. Michel, “Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach,” International Journal of Systems Science, vol. 32, no. 8, pp. 1055–1061, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. B. Lu and F. Wu, “Switching LPV control designs using multiple parameter-dependent Lyapunov functions,” Automatica, vol. 40, no. 11, pp. 1973–1980, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S.-H. Lee, T.-H. Kim, and J.-T. Lim, “A new stability analysis of switched systems,” Automatica, vol. 36, no. 6, pp. 917–922, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. Ji and L. Wang, “Quadratic stabilization of uncertain discrete-time switched linear systems,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC '04), pp. 1492–1497, October 2004. View at Scopus
  19. G. Xie and L. Wang, “Stabilization of a class of hybrid discrete-time systems,” in Proceedings of the 2003 IEEE Conference on Control Applications, pp. 1404–1409, June 2003. View at Scopus
  20. G. Zhai, H. Lin, A. N. Michel, and K. Yasuda, “Stability analysis for switched systems with continuous-time and discrete-time subsystems,” in Proceedings of the American Control Conference (AAC '04), pp. 4555–4560, July 2004. View at Scopus
  21. J. Daafouz, P. Riedinger, and C. Iung, “Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1883–1887, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  22. D. Xie, L. Wang, F. Hao, and G. Xie, “LMI approach to L2-gain analysis and control synthesis of uncertain switched systems,” IEE Proceedings, vol. 151, no. 1, pp. 21–28, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. D. Xie, L. Wang, F. Hao, and G. Xie, “Robust stability analysis and control synthesis for discrete-time uncertain switched systems,” in Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 4812–4817, December 2003. View at Scopus
  24. Z. Sun, “Sampling and control of switched linear systems,” Journal of the Franklin Institute, vol. 341, no. 7, pp. 657–674, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. S. Mahmoud, M. F. Hassan, and M. G. Darwish, Large-Scale Control Systems, Marcel Dekker, New York, NY, USA, 1985.
  26. M. Y. Waziri and Z. A. Majid, “An improved diagonal Jacobian approximation via a new Quasi-Cauchy condition for solving large-scale systems of nonlinear equations,” Journal of Applied Mathematics, vol. 2013, Article ID 875935, 6 pages, 2013. View at Publisher · View at Google Scholar
  27. B. Labibi, “Decentralized control via disturbance attenuation and eigenstructure assignment,” IEEE Transactions on Circuits and Systems II, vol. 53, no. 6, pp. 468–472, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. S. Xie and L. Xie, “Stabilization of a class of uncertain large-scale stochastic systems with time delays,” Automatica, vol. 36, no. 1, pp. 161–167, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. W.-J. Wang and L.-G. Mau, “Stabilization and estimation for perturbed discrete time-delay large-scale systems,” IEEE Transactions on Automatic Control, vol. 42, no. 9, pp. 1277–1282, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. S. Xie and L. Xie, “Decentralized stabilization of a class of interconnected stochastic nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 1, pp. 132–137, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. S. Xie, L. Xie, Y. Wang, and G. Guo, “Decentralized control of multimachine power systems with guaranteed performance,” IEE Proceedings, vol. 147, no. 3, pp. 355–365, 2000.
  32. H. Wu, “Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections,” IEEE Transactions on Automatic Control, vol. 47, no. 10, pp. 1745–1751, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. W. J. Wang and L. Luoh, “Stability and stabilization of fuzzy large-scale systems,” IEEE Transactions on Fuzzy Systems, vol. 12, no. 3, pp. 309–315, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. K. Zhou and P. P. Khargonekar, “Robust stabilization of linear systems with norm-bounded time-varying uncertainty,” Systems and Control Letters, vol. 10, no. 1, pp. 17–20, 1988. View at Zentralblatt MATH · View at MathSciNet · View at Scopus