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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 595029, 10 pages
http://dx.doi.org/10.1155/2013/595029
Research Article

On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties

1Department of Academic Areas of Jataí, Federal Institute of Education, Science and Technology of Goiás (IFG), Campus Jataí, 75804-020 Jataí, GO, Brazil
2Department of Electrical Engineering, UNESP, Univ Estadual Paulista, Campus de Ilha Solteira, 15385-000 Ilha Solteira, SP, Brazil
3Department of Computer, Telecommunication, Control, and Automation Engineering, Faculdade of Science and Technology of Montes Claros (FACIT), Campus II, 39400-141 Montes Claros, MG, Brazil

Received 17 January 2013; Accepted 12 April 2013

Academic Editor: Oleg V. Gendelman

Copyright © 2013 Wallysonn A. de Souza 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. M. A. Wicks, P. Peleties, and R. A. DeCarlo, “Construction of piecewise Lyapunov functions for stabilizing switched systems,” in Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 4, pp. 3492–3497, December 1994. View at Scopus
  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. R. A. Decarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, “Perspectives and results on the stability and stabilizability of hybrid systems,” Proceedings of the IEEE, vol. 88, no. 7, pp. 1069–1082, 2000. View at Scopus
  4. J. P. Hespanha and A. S. Morse, “Switching between stabilizing controllers,” Automatica, vol. 38, no. 11, pp. 1905–1917, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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 · View at Scopus
  6. A. Feuer, G. C. Goodwin, and M. Salgado, “Potential benefits of hybrid control for linear time invariant plants,” in Proceedings of the American Control Conference (ACC '97), vol. 5, pp. 2790–2794, June 1997. View at Scopus
  7. N. H. Mcclamroch and I. Kolmanovsky, “Performance benefits of hybrid control design for linear and nonlinear systems,” Proceedings of the IEEE, vol. 88, no. 7, pp. 1083–1096, 2000. View at Scopus
  8. H. Ishii and B. A. Francis, “Stabilizing a linear system by switching control with dwell time,” IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 1962–1973, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. D. J. Leith, R. N. Shorten, W. E. Leithead, O. Mason, and P. Curran, “Issues in the design of switched linear control systems: a benchmark study,” International Journal of Adaptive Control and Signal Processing, vol. 17, no. 2, pp. 103–118, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Pettersson, “Controller design of switched linear systems,” in Proceedings of the American Control Conference (AAC '04), vol. 4, pp. 3869–3874, Boston, Mass, USA, July 2004. View at Scopus
  11. H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. C. Geromel and G. S. Deaecto, “Switched state feedback control for continuous-time uncertain systems,” Automatica, vol. 45, no. 2, pp. 593–597, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. N. Otsuka and T. Soga, “Quadratic stabilizability for polytopic uncertain continuoustime switched linear systems composed of two subsystems,” International Journal of Control and Automation, vol. 3, no. 1, pp. 35–42, 2010.
  14. G. S. Deaecto, J. C. Geromel, and J. Daafouz, “Switched state-feedback control for continuous time-varying polytopic systems,” International Journal of Control, vol. 84, no. 9, pp. 1500–1508, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. Xie and M. Yu, “Stability analysis of switched linear systems with polytopic uncertainties,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC '06), vol. 5, pp. 3749–3753, October 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. G. Zhai, H. Lin, and P. J. Antsaklis, “Quadratic stabilizability of switched linear systems with polytopic uncertainties,” International Journal of Control, vol. 76, no. 7, pp. 747–753, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1994.
  18. J. Löfberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceedings of the 2004 IEEE International Symposium on Computer Aided Control System Design, pp. 284–289, September 2004. View at Scopus
  19. J. F. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimization Methods and Software, vol. 11-12, no. 1, pp. 625–653, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. J. Bernussou, P. L. D. Peres, and J. C. Geromel, “A linear programming oriented procedure for quadratic stabilization of uncertain systems,” Systems and Control Letters, vol. 13, no. 1, pp. 65–72, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. D. D. Šiljak and D. M. Stipanović, “Robust stabilization of nonlinear systems: the LMI approach,” Mathematical Problems in Engineering, vol. 6, no. 5, pp. 461–493, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. R. Cardim, M. C. M. Teixeira, E. Assuncao et al., “Implementation of a DC-DC converter with variable structure control of switched systems,” in Proceedings of the IEEE International Electric Machines Drives Conference (IEMDC '11), pp. 872–877, Niagara Falls, Canada, May 2011.
  23. R. Cardim, M. C. M. Teixeira, E. Assunção, et al., “Design and implementation of a DC-DC converter based on variable structure control of switched systems,” in 18th IFAC World Congress, vol. 18, pp. 11048–11054, Milan, Italy, 2011.
  24. B. R. Barmish, “Stabilization of uncertain systems via linear control,” IEEE Transactions on Automatic Control, vol. 28, no. 8, pp. 848–850, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. J. Corless and G. Leitmann, “Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems,” IEEE Transactions on Automatic Control, vol. 26, no. 5, pp. 1139–1144, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. M. P. A. Santim, M. C. M. Teixeira, W. A. de Souza, R. Cardim, and E. Assunção, “Design of a Takagi-Sugeno fuzzy regulator for a set of operation points,” Mathematical Problems in Engineering, vol. 2012, Article ID 731298, 17 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  27. R. Cardim, M. C. M. Teixeira, E. Assunção, and M. R. Covacic, “Variable-structure control design of switched systems with an application to a DC-DC power converter,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3505–3513, 2009. View at Publisher · View at Google Scholar · View at Scopus