Abstract
This paper deals with a LQR problem for 2D (2-dimensional) systems in the case that one independent variable is bounded but the other is unbounded. First, we formulate the 2D LQR problem for Roesser model. Then it is shown that the problem can be reduced to an equivalent LQR problem for 1D systems, and thus, can be solved by 1D theory. The obtained controller has one direction causality. The relationship between the solvability conditions obtained for the equivalent 1D system and the practical stabilizability and detectability of the original 2D plant is clarified. Based on these results, its application to the design of an iterative learning control system is shown. Finally, a numerical example is also given to verify the effectiveness.
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