Multidimensional Systems and Signal Processing, Vol. 19, pp. 449-475, 2008. A geometric theory for 2-D systems including notions of stabilisability L. Ntogramatzidis, M. Cantoni, R. Yang Abstract In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini-Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint. Key words: 2-D Fornasini-Marchesini models, Controlled invariance, Output-nulling subspaces, Internal/external stabilisation, Disturbance decoupling problems