`ISRN Applied MathematicsVolume 2012 (2012), Article ID 365927, 18 pagesdoi:10.5402/2012/365927`
Research Article

## Repetitive Processes Based Iterative Learning Control Designed by LMIs

Laboratory of Analysis and Control of Systems (LACS), National Engineering School of Tunis, BP 37, le Belvedere, 1002 Tunis, Tunisia

Received 20 October 2012; Accepted 12 November 2012

Academic Editors: Y. Dimakopoulos, Z. Hou, and C. Lu

Copyright © 2012 Jamel Dridi 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.

1. S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operations of robots by learning,” Journal of Robotic Systems, vol. 1, no. 2, pp. 123–140, 1984.
2. E. Fornasini and G. Marchesini, “State-space realization theory of two-dimensional filters,” IEEE Transactions on Automatic Control, vol. 21, no. 4, pp. 484–492, 1976.
3. M. Norrlf, Iterative learning control, analysis, design and experiments [Ph.D. thesis], Linköping University, Linkopings, Sweden, 2000.
4. D. H. Owens, N. Amann, E. Rogers, and M. French, “Analysis of linear iterative learning control schemes—a 2D systems/repetitive processes approach,” Multidimensional Systems and Signal Processing, vol. 11, no. 1-2, pp. 125–177, 2000.
5. K. L. Moore, Iterative Learning Control for Deterministic Systems, Advances in Industrial Control Series, Springer, London, UK, 1993.
6. K. Gakowski, R. W. Longman, and E. Rogers, “Special issue: multidimensional systems (nD) and iterative learning control,” International Journal of Applied Mathematics and Computer Science, vol. 13, no. 1, 2003.
7. E. Rogers, K. Galkowski, and D. H. Owens, Control Systems Theory and Applications for Linear Repetitive Processes, vol. 349 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2007.
8. P. D. Roberts, “Two-dimensional analysis of an iterative nonlinear optimal control algorithm,” IEEE Transactions on Circuits and Systems, vol. 49, no. 6, pp. 872–882, 2002, Special issue on multidimensional signals and systems.
9. J. Xu, M. Sun, and L. Yu, “LMI-based robust iterative learning controller design for discrete linear uncertain systems,” Journal of Control Theory and Applications, vol. 3, no. 3, pp. 259–265, 2005.
10. H. S. Ahn, K. L. Moore, and Y. Chen, “LMI approach to iterative learning control design,” in Proceedings of the IEEE Mountain Workshop on Adaptive and Learning Systems (SMCals '06), pp. 72–77, July 2006.
11. A. Rantzer, “On the Kalman-Yakubovich-Popov lemma,” Systems & Control Letters, vol. 28, no. 1, pp. 7–10, 1996.
12. B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control. Theory and Applications, Communications and Control Engineering Series, Springer, London, UK, 2nd edition, 2007.
13. T. Iwasaki and S. Hara, “Generalized KYP lemma: unified frequency domain inequalities with design applications,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 41–59, 2005.
14. E. Rogers and D. H. Owens, Stability Analysis for Linear Repetitive Processes, vol. 175 of Lecture Notes in Control and Information Sciences, Springer, Berlin, UK, 1992.
15. W. Paszke, P. Rapisarda, E. Rogers, and M. Steinbuch, “Using dissipativity theory to formulate necessary and sufficient conditions for stability of linear repetitive processes,” Research Report, School of Electronics and Computer Science, University of Southampton, Hampshire, UK, 2008.
16. T. Iwasaki, G. Meinsma, and M. Fu, “Generalized $S$-procedure and finite frequency KYP lemma,” Mathematical Problems in Engineering, vol. 6, no. 2-3, pp. 305–320, 2000.
17. J. E. Kurek and M. B. Zaremba, “Iterative learning control synthesis based on 2-D system theory,” IEEE Transactions on Automatic Control, vol. 38, no. 1, pp. 121–125, 1993.
18. P. Gahinet and P. Apkarian, “A linear matrix inequality approach to h$\infty$ control,” International Journal of Robust and Nonlinear Control, vol. 4, no. 4, pp. 421–448, 1994.
19. L. Hladowski, Z. Cai, K. Galkowski et al., “Repetitive process based iterative learning control designed by LMIs and experimentally verified on a gantry robot,” in American Control Conference (ACC '09), pp. 949–954, Institute of Control and Computation Engineering of the University of Zielona, June 2009.
20. R. C. Dorf and R. H. Bishop, Modern Control Systems, Prentice Hall, 10th edition, 2004.