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Mathematical Problems in Engineering
Volume 2014, Article ID 970841, 5 pages
Research Article

Iterative Learning Control Design and Application for Linear Continuous Systems with Variable Initial States Based on 2-D System Theory

1Beijing Institute of Control Engineering, Beijing 100190, China
2School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received 14 February 2014; Revised 22 April 2014; Accepted 12 May 2014; Published 22 May 2014

Academic Editor: Xinzhu Meng

Copyright © 2014 Wei Guan 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.


This paper is concerned with the variable initial states problem in iterative learning control (ILC) for linear continuous systems. Firstly, the properties of the trajectory of 2-D continuous-discrete Roesser model are analyzed by using Lyapunov's method. Then, for any variable initial states which absolutely converge to the desired initial state, some ILC design criteria in the form of linear matrix inequalities (LMI) are given to ensure the convergence of the PD-type ILC rules. The convergence for variable initial states implies that the ILC rules can be used to achieve the perfect tacking for variable initial states, even if the system dynamic is unknown. Finally, the micropropulsion system is considered to illustrate efficiency of the proposed ILC design criteria.