The subject of this chapter is to find a minimal state-space representation of a transfer function matrix. The chapter addresses two approaches: the representation of an LTI MIMO systems as a superposition of single-input-multiple-output (SIMO) systems and Gilbert’s minimal state-space realisation. If there are two minimal state-space realisations of order n of a transfer function matrix, then they are equivalent. A unique non-singular matrix can be found that transforms one representation into the other. In the case that a state-space realisation of a transfer function matrix is found not to be fully state controllable or not fully state observable, it can be reduced to a minimal one by the Octave command minreal().