Design of ILC laws with conditions for stabilizing linear 2D discrete Roesser models

This paper considers the design of iterative learning control schemes by transforming the task into an equivalent problem of designing stabilizing control laws for the Roesser model for linear two-dimensional systems. Then, based on a non-conservative version of stability and stabilization conditions for linear 2D systems, a control law is designed based on linear matrix inequalities. In addition, some control performance indexes are improved by choosing the locations for the relevant transfer function, leading to faster convergence. Also, an additional linear matrix inequality constraint is developed to minimize the gain of designed controllers and facilitate their practical implementation. Furthermore, the problem of ILC control law design for strictly proper system dynamics using anticipative action. Finally, a numerical example demonstrates the effectiveness of the new results, including advantages when compared to the existing alternatives.