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Zbl 1122.93346
Xu, Jianming; Sun, Mingxuan; Li, Yu
LMI-based robust iterative learning controller design for discrete linear uncertain systems.
(English)
[J] J. Control Theory Appl. 3, No. 3, 259-265 (2005). ISSN 1672-6340

Summary: This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learning control (ILC) system is reformulated as a $\gamma$-suboptimal $H_\infty$ control problem via the linear fractional transformation (LFT). A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities (LMIs). Furthermore, the linear transfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The results demonstrate the effectiveness of the proposed method.
MSC 2000:
*93B51 Design techniques in systems theory
93C55 Discrete-time control systems
93D09 Robust stability of control systems
93C41 Control problems with incomplete information

Keywords: iterative learning control; $H_\infty$ control; linear fractional transformation; linear matrix inequality (LMI)

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