The MSDOS project questions the stability and stabilization of multidimensional systems also known as nD systems. It is aimed at expanding both the theoretical and practical aspect of the field. MSDOS is decomposed into 6 different tasks. Three tasks are indeed devoted to advance the theory of multidimensional systems in stability and stabilization: one based on the Lyapunov theory, one focused on repetitive systems and one using a fractional representation approach. The last three ones are focused on the practical aspects of the field: first the results obtained will be applied to study other infinite dimensional systems using an nD approach, second a set of packages will be proposed for analysis and synthesis problems, and simulation of nD systems, third the creation of a complete course on multidimensional systems will be available at least in one of the partner laboratory. The project should significantly help creating a stronger community of researcher in France around this exciting field which is one of the main goals of the project on par with the obtained theoretical advances. The work will be handled by four different partners with complementary skills starting with LIAS in Poitiers (and LATP in Marseille), INRIA Saclay-Île-de-France in Paris, XLIM (Limoges) and an international collaboration with ISSI (Poland).