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An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

Mojtaba Ayatinia, Mehdi Forouzanfar*, and Amin Ramezani
International Journal of Control, Automation, and Systems, vol. 20, no. 7, pp.2391-2401, 2022

Abstract : This paper presents a new robust convergence condition of iterative learning control (ILC) for linear multivariable discrete-time systems in the presence of iteration-varying uncertainty. This method is based on linear matrix inequality (LMI) and provides a fixed learning gain over time and iteration. Since the convergence of the ILC algorithm may change due to uncertainty in the parameters of a system, and the ILC algorithm is incapable of dealing with iteration-related challenges, it is a major challenge to reject the effect of iteration varying uncertainty. In this paper, first, a convergence condition of the ILC algorithm is designed based on closed-loop system stability in the iteration domain, and second, a new robust convergence condition is achieved by the LMI approach. Finally, the effectiveness of the proposed robust convergence scheme is evaluated through two numerical examples.

Keyword : "Fixed learning gain, iteration-varying uncertainty, iterative learning control (ILC), linear matrix inequality (LMI), robust convergence. "

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