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The aim of this work is to develop a design procedure for a networked system composed by 2-d (2-dimensional) observer controller and 2-d linear discrete system, which are located apart from each other. The Lagrange method, which is a framework for solving multidimensional linear discrete system equations, is the main tool for handling the composite system. We also show along the investigation that the procedure depends on the type of the matrix B which weights the input of the system. Finally, the execution of the design algorithm is demonstrated with a numerical example.