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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 528695, 9 pages
http://dx.doi.org/10.1155/2013/528695
Research Article

Control of Discrete-Time Singularly Perturbed Systems via Static Output Feedback

State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China

Received 19 December 2012; Accepted 22 February 2013

Academic Editor: Guanglu Zhou

Copyright © 2013 Dan Liu 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. S. Sen and K. B. Datta, “Stability bounds of singularity perturbed systems,” Transactions on Automatic Control, vol. 38, no. 2, pp. 302–304, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B.-S. Chen and C. L. Lin, “On the stability bounds of singularly perturbed systems,” Transactions on Automatic Control, vol. 35, no. 11, pp. 1265–1270, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. Q. Liu and V. Sreeram, “A new characterization on stability bounds for singularly perturbed systems,” Linear Algebra and Its Applications, vol. 263, pp. 377–388, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  4. W. Q. Liu, M. Paskota, V. Sreeram, and K. L. Teo, “Improvement on stability bounds for singularly perturbed systems via state feedback,” International Journal of Systems Science, vol. 28, no. 6, pp. 571–578, 1996. View at Scopus
  5. J. C. Geromel, C. C. de Souza, and R. E. Skelton, “Static output feedback controllers: stability and convexity,” Transactions on Automatic Control, vol. 43, no. 1, pp. 120–125, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. Shi and V. Dragan, “Asymptotic H control of singularly perturbed systems with parametric uncertainties,” Transactions on Automatic Control, vol. 44, no. 9, pp. 1738–1742, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. G. Xu, “Exponential p-stability of singularly perturbed impulsive stochastic delay differential systems,” International Journal of Control, Automation, and Systems, vol. 9, pp. 966–972, 2011.
  8. W. H. Chen, G. Yuan, and W. X. Zheng, “Robust stability of singularly perturbed impulsive systems under nonlinear perturbation,” IEEE Transactions on Automatic Control, vol. 58, pp. 168–174, 2013.
  9. C. Yang, J. Sun, and X. Ma, “Stabilization bound of singularly perturbed systems subject to actuator saturation,” Automatica, vol. 49, no. 2, pp. 457–462, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  10. F. Hachemi, M. Sigalotti, and J. Daafouz, “Stability analysis of singularly perturbed switched linear systems,” Transactions on Automatic Control, vol. 57, no. 8, pp. 2116–2121, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Dong and G.-H. Yang, “Robust H control for standard discrete-time singularly perturbed systems,” IET Control Theory & Applications, vol. 1, no. 4, pp. 1141–1148, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Dong and G.-H. Yang, “H control for fast sampling discrete-time singularly perturbed systems,” Automatica, vol. 44, no. 5, pp. 1385–1393, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Xu and G. Feng, “New results on H control of discrete singularly perturbed systems,” Automatica, vol. 45, no. 10, pp. 2339–2343, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Ivan and J. Daafouz, “Stabilisation of polytopic singularly perturbed linear systems,” International Journal of Control, vol. 85, no. 2, pp. 135–142, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. R. Vrabel, “On the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems,” Systems & Control Letters, vol. 61, no. 3, pp. 422–426, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Chen, F. Sun, Y. Yin, and C. Hu, “State feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems with parameter uncertainty,” IET Control Theory & Applications, vol. 5, no. 10, pp. 1195–1202, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  17. D. Mehdi, E. K. Boukas, and O. Bachelier, “Static output feedback design for uncertain linear discrete time systems,” IMA Journal of Mathematical Control and Information, vol. 21, no. 1, pp. 1–13, 2003. View at Zentralblatt MATH · View at MathSciNet
  18. Q. L. Han, “A delay decomposition approach to stability and H control of linear time-delay systems—part II: H control,” in Proceedings of the 7th World Congress on Intelligent Control and Automation (WCICA '08), pp. 289–294, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. P. Gahinet and P. Apkarian, “A linear matrix inequality approach to H control,” International Journal of Robust and Nonlinear Control, vol. 4, no. 4, pp. 421–448, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. E. K. Boukas, “Static output feedback control for linear descriptor systems: LMI approach,” in Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA '05), vol. 3, pp. 1230–1234, August 2005. View at Scopus