Definition (Realization)

Given a mapping $T:J\times J\to M_{p\times n}(\mathbb{R})$ we say a realization of T is any triple $(A,B,C)$ s.t. the following holds $$T(t,\tau)=C(t)\Phi_{A}(t,\tau)B(\tau)$$

Definition (Realizable)

Given a mapping $T:J\times J\to M_{p\times n}(\mathbb{R})$ we say $T$ is realizable if $\exists(A,B,C)$ Continuous maps s.t. the following holds $$T(t,\tau)=C(t)\Phi_{A}(t,\tau)B(\tau)$$