The purpose of the thesis is to develop a comprehensive theory of the geometric control for N-dimensional systems. Two possible representations and their structural invariance properties of 2-D systems will be considered and generalised to the N-dimensional case: the Fornasini-Marchesini first order model and Fornasini-Marchesini second order model. In addition, necessary and sufficient conditions for the existence of solutions for the implicit 2-D Fornasini-Marchesini models will be provided, and generalised to the N-dimensional case
