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Mathematical Problems in Engineering
Volume 2015, Article ID 854306, 8 pages
http://dx.doi.org/10.1155/2015/854306
Research Article

Synthesis of Adaptive Gain Robust Controllers for Polytopic Uncertain Systems

1The Institute of Technology and Science, Tokushima University, 2-1 Minamijosanjima, Tokushima 770-8506, Japan
2The Graduate School of Advanced Technology and Science, Tokushima University, 2-1 Minamijosanjima, Tokushima 770-8506, Japan
3The Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, Japan

Received 25 September 2014; Accepted 5 January 2015

Academic Editor: Bin Jiang

Copyright © 2015 Hidetoshi Oya 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. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, 1996.
  2. I. 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 Publisher · View at Google Scholar · View at MathSciNet
  3. W. E. Schmitendorf, “Designing stabilizing controllers for uncertain systems using the Riccati equation approach,” IEEE Transactions on Automatic Control, vol. 33, no. 4, pp. 376–379, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · 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 MathSciNet · View at Scopus
  5. P. P. Khargonekar, I. R. Petersen, and K. Zhou, “Robust stabilization of uncertain linear systems: quadratic stabilizability and H control theory,” IEEE Transactions on Automatic Control, vol. 35, no. 3, pp. 356–361, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. S. Chang and T. K. C. Peng, “Adaptive guaranteed cost control of systems with uncertain parameters,” IEEE Transactions on Automatic Control, vol. 17, no. 4, pp. 474–483, 1972. View at Google Scholar · View at MathSciNet
  7. I. R. Petersen and D. C. McFarlane, “Optimal guaranteed cost control and filtering for uncertain linear systems,” IEEE Transactions on Automatic Control, vol. 39, no. 9, pp. 1971–1977, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. L. Yu and J. Chu, “An LMI approach to guaranteed cost control of linear uncertain time-delay systems,” Automatica, vol. 35, no. 6, pp. 1155–1159, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. Chilali and P. Gahinet, “H design with pole placement constraints: an LMI approach,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 358–367, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. Chilali, P. Gahinet, and P. Apkarmann, “Robust pole placement in LMI regions: an LMI approach,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 2257–2270, 1999. View at Google Scholar
  11. 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 Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. H. Oya and K. Hagino, “Robust control with adaptive compensation input for linear uncertain systems,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 86, no. 6, pp. 1517–1524, 2003. View at Google Scholar · View at Scopus
  13. H. Oya and Y. Uehara, “Synthesis of variable gain controllers based on LQ optimal control for a class of uncertain linear systems,” in Proceedings of the UKACC International Conference on Control (CONTROL '12), pp. 87–91, Cardiff, UK, September 2012. View at Publisher · 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 International Conference on Cybernetics and Information Technologies, Systems and Applications, vol. 2, pp. 324–329, 2004.
  15. 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 Scopus
  16. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, Society for Industrial and Applied Mathematics, 1994.
  17. H. Oya, K. Hagino, and M. Matsuoka, “Observer-based guaranteed cost control scheme for polytopic uncertain systems with state delays,” in Proceedings of the 30th Annual Conference of the IEEE Industrial Electronics Society (IECON '04), p. TA6-5, Busan, Republic of Korea, 2004.