Improved LMI-based conditions for designing of PD-type ILC laws for linear batch processes over two-dimensional setting

This paper considers the problem of designing of iterative learning control (ILC) laws for linear batch processes. Unlike the majority of existing results about ILC law design for linear batch processes over repetitive/two-dimensional setting where Lyapunov theory is applied, this study is focused on formulating the ILC law design procedures by transforming it into an equivalent problem of (structural) stability analysis for a linear Roesser model for two-dimensional (2D) systems. Then, based on a non-conservative version of stability and stabilization conditions for linear 2D systems, suitable PD-type ILC laws are derived by the application of the linear matrix inequality (LMI) approach. Finally, a numerical example is given to show the validity of the proposed design procedure and some advantages are emphasized when compared to the existing alternatives.