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This paper addresses the issue of polynomial iterative learning tracking control (Poly-ILC) for continuous-time linear systems (LTI) operating repetitively. It explores the design of an iterative learning control law by examining the stability along the pass theory of 2D repetitive systems. The obtained result is a generalization of the notion of stability along passages, taking into account transient performances. To strike a balance between stability along passages and transient performance, we extend our developed result in the discrete case, relying on some numerical tools. Specifically, in this work we investigate the convergence of tracking error with given learning controller gains. The key contribution of this structure of control lies in establishing an LMI (linear matrix inequality) condition that ensures both pole placement according to desired specifications and the convergence of output error between iterations. Furthermore, new sufficient conditions for stability regions along the pass addressing the tracking problem of differential linear repetitive processes are developed. Numerical results are provided to demonstrate the effectiveness of the proposed approaches.
Attia et al. (Tue,) studied this question.