A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
The notion of the normal transfer matrix and the notion of the structure decomposition of normal transfer matrix for 2D general model are introduced. Necessary and suﬃcient conditions for the existence of the structure decomposition of normal transfer matrix are established. A procedure for computation of the structure decomposition is proposed and illustrated by the numerical example. It is shown that the impulse response matrix of the normal model is independent of the polynomial part of its structure decomposition.