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Journal of Control Science and Engineering
Volume 2012, Article ID 902576, 10 pages
http://dx.doi.org/10.1155/2012/902576
Research Article

Synthesis of Adaptive Gain Robust Output Feedback Controllers for a Class of Lipschitz Nonlinear Systems with Unknown Upper Bound of Uncertainty

1Institute of Technology and Science, The University of Tokushima, 2-1 Minamijosanjima, Tokushima 770-8506, Japan
2Department of Systems Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan

Received 9 May 2012; Accepted 6 July 2012

Academic Editor: Zhiyong Chen

Copyright © 2012 Hidetoshi Oya and Kojiro Hagino. 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. K. Zhou, Essentials of Robust Control, Prentice Hall, Upper Saddle River, NJ, USA, 1998.
  2. B. R. Barmish, “Stabilization of uncertain systems via linear control,” IEEE Transactions on Automatic Control, vol. 8, no. 8, pp. 848–850, 1983. View at Google Scholar · View at Scopus
  3. I. R. Petersen and C. V. Hollot, “A riccati equation approach to the stabilization of uncertain linear systems,” Automatica, vol. 22, no. 4, pp. 397–411, 1986. View at Google Scholar · View at Scopus
  4. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H control problems,” IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831–847, 1989. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Yamamoto and K. Yamauchi, “A design method of adaptive control systems by a time-varying parameter of robust stabilizing state feedback,” Transactions of the Institute of Systems, Control and Information Engineers, vol. 12, no. 6, pp. 319–325, 1999 (Japanese). View at Google Scholar
  6. M. Maki and K. Hagino, “Robust control with adaptation mechanism for improving transient behaviour,” International Journal of Control, vol. 72, no. 13, pp. 1218–1226, 1999. View at Google Scholar · View at Scopus
  7. H. Oya and K. Hagino, “Robust control with adaptive compensation input for linear uncertain systems,” Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 86, no. 6, pp. 1517–1524, 2003. View at Google Scholar · View at Scopus
  8. H. Oya and K. Hagino, “Adaptive robust control scheme for linear systems with structured uncertainties,” Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 87, no. 8, pp. 2168–2173, 2004. View at Google Scholar · View at Scopus
  9. J. R. Petersen, “A riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems,” IEEE Transactions on Automatic Control, vol. 30, no. 9, pp. 904–907, 1985. View at Google Scholar · View at Scopus
  10. H. Oya and K. Hagino, “Observer-based robust control giving consideration to transient behaviour for linear systems with structured uncertainties,” International Journal of Control, vol. 75, no. 15, pp. 1231–1240, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. S. O. R. Moheimani and I. R. Petersen, “Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback,” Automatica, vol. 32, no. 4, pp. 575–579, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. J. C. Geromel, C. C. De Souza, and R. E. Skelton, “LMI numerical solution for output feedbadck stabilization,” in Proceedings of the American Control Conference, pp. 40–44, Baltimore, Md, USA, 1994.
  13. T. Iwasaki, R. E. Skelton, and J. C. Geromel, “Linear quadratic suboptimal control with static output feedback,” Systems and Control Letters, vol. 23, no. 6, pp. 421–430, 1994. View at Google Scholar · View at Scopus
  14. M. Matsuoka and K. Hagino, “A robust control design via a variable gain controller using an observer without information on the upper bound of uncertainties,” in Proceedings of the 10th International Conference on Information System Analysis and Synthesis, pp. 324–329, 2004.
  15. H. Oya, K. Hagino, and S. Kayo, “Synthesis of adaptive robust output feedback controllers for a class of uncertain linear systems,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 995–1000, Cancun, Mexico, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. F. Mazenc, L. Praly, and W. P. Dayawansa, “Global stabilization by output feedback: examples and counterexamples,” Systems and Control Letters, vol. 23, no. 2, pp. 119–125, 1994. View at Google Scholar · View at Scopus
  17. A. N. Atassi and H. K. Khalil, “A separation principle for the stabilization of a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1672–1687, 1999. View at Google Scholar · View at Scopus
  18. L. Praly, “Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate,” in Proceedings of the 40th IEEE Conference on Decision and Control (CDC '01), pp. 3808–3813, Orlando, Fla, USA, December 2001. View at Scopus
  19. C. Qian, “A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems,” in Proceedings of the American Control Conference (ACC '05), pp. 4708–4715, Portland, Ore, USA, June 2005. View at Scopus
  20. J. Polendo and C. Qian, “A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback,” International Journal of Robust and Nonlinear Control, vol. 17, no. 7, pp. 605–629, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Li and C. Qian, “Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 879–884, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Tsinias, “Backstepping design for time-varying nonlinear systems with unknown parameters,” Systems and Control Letters, vol. 39, no. 4, pp. 219–227, 2000. View at Google Scholar · View at Scopus
  23. H. L. Choi and J. T. Lim, “Output feedback stabilization for a class of Lipschitz nonlinear systems,” Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 88, no. 2, pp. 602–605, 2005. View at Google Scholar · View at Scopus
  24. H. Oya and K. Hagino, “Synthesis of variable gain robust output feedback controllers for a class of uncertain lipschitz nonlinear systems,” in Proceedings of the 9th International Conference on Control & Automation, pp. 698–703, Santiago, Chile, December 2011.
  25. F. R. Gantmacher, The Theory of Matrices, vol. 1, Chelsea Publishing Company, New York, NY, USA, 1960.
  26. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathmatics, 1994.
  27. H. K. Khalil, Nonlinear Systems, Prentice Hall, 3rd edition, 2002.
  28. V. Kučera and C. E. De Souza, “A necessary and sufficient condition for output feedback stabilizability,” Automatica, vol. 31, no. 9, pp. 1357–1359, 1995. View at Google Scholar · View at Scopus
  29. R. E. Benton and D. Smith, “Non-iterative LMI-based algorithm for robust static-output-feedback stabilization,” International Journal of Control, vol. 72, no. 14, pp. 1322–1330, 1999. View at Publisher · View at Google Scholar · View at Scopus