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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 39367, 15 pages
http://dx.doi.org/10.1155/MPE/2006/39367

Stability and stabilization of continuous descriptor systems: An LMI approach

1Automatic Control Unit, Sfax Preparatory Institute for Engineering Studies (IPEIS), Sfax University, BP 805, Sfax 3018, Tunisia
2Laboratory of Automatic Control and Computer Science for Industry (LAII), Higher Engineering School of Poitiers (ESIP), University of Poitiers, 40 Avenue du Recteur Pineau, Poitiers Cedex 86022, France

Received 8 February 2005; Revised 19 November 2005; Accepted 24 January 2006

Copyright © 2006 M. Chaabane 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. O. Bachelier, J. Bernussou, M.-C. de Oliveira, and J.-C. Geromel, “Parameter dependent Lyapunov control design: numerical evaluation,” in Proceedings of the 38th IEEE Conference on Decision & Control, pp. 293–297, Arizona, December 1999. View at Google Scholar
  2. B. R. Barmish, “Necessary and sufficient conditions for quadratic stabilizability of an uncertain system,” Journal of Optimization Theory and Applications, vol. 46, no. 4, pp. 399–408, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. P. Bernhard, “On singular implicit linear dynamical systems,” SIAM Journal on Control and Optimization, vol. 20, no. 5, pp. 612–633, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Daafouz and J. Bernussou, “Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties,” Systems & Control Letters, vol. 43, no. 5, pp. 355–359, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Dai, Singular Control Systems, vol. 118 of Lecture Notes in Control and Information Sciences, Springer, Berlin, 1989. View at Zentralblatt MATH · View at MathSciNet
  6. P. Gahinet, P. Apkarian, and M. Chilali, “Affine parameter-dependent Lyapunov functions and real parametric uncertainty,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 436–442, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-C. Geromel, M.-C. de Oliveira, and L. Hsu, “LMI characterization of structural and robust stability,” Linear Algebra and Its Applications, vol. 285, no. 1–3, pp. 69–80, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Y. Ishihara and M. H. Terra, “On the Lyapunov theorem for singular systems,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1926–1930, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C.-H. Kuo and C.-H. Fang, “An LMI approach to admissibilization of unceratin descriptor systems via static output feedback,” in Proceedings of the American Control Conference, vol. 6, pp. 5104–5109, Colorado, June 2003, FP06. View at Google Scholar
  10. F. L. Lewis, “A survey of linear singular systems,” Circuits, Systems, and Signal Processing, vol. 5, no. 1, pp. 3–36, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. Lin, Q.-G. Wang, and T. H. Lee, “Robust normalization and stabilization of uncertain descriptor systems with norm-bounded perturbations,” IEEE Transactions on Automatic Control, vol. 50, no. 4, pp. 515–520, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  12. I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, “H control for descriptor systems: a matrix inequalities approach,” Automatica, vol. 33, no. 4, pp. 669–673, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. E. Skelton, T. Iwasaki, and K. M. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, The Taylor & Francis Systems and Control Book Series, Taylor & Francis, London, 1998. View at MathSciNet
  14. K. Takaba, N. Morihira, and T. A. Katayama, “A generalized Lyapunov theorem for descriptor system,” Systems & Control Letters, vol. 24, no. 1, pp. 49–51, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. Varga, “On stabilization methods of descriptor systems,” Systems & Control Letters, vol. 24, no. 2, pp. 133–138, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. 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 Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. Xu and J. Lam, “Robust stability and stabilization of discrete singular systems: an equivalent characterization,” IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 568–574, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. Yu, “Regularizability of linear time-invariant descriptor systems under decentralized control,” Automatica, vol. 41, no. 9, pp. 1639–1644, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  19. K. Zhou, J.-C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, New Jersey, 1996. View at Zentralblatt MATH
  20. K. Zhou and P. P. Khargonekar, “Robust stabilization of linear systems with norm-bounded time-varying uncertainty,” Systems & Control Letters, vol. 10, no. 1, pp. 17–20, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet