103 Transfer function of a Laplace transformed system

Consider a linear system $Y=LU$ where $L$ is a linear operator, and such that all the entries of the $(k\times 1)$ input $U$ and $(m\times 1)$ output $Y$ satisfy $(E)$, and let the initial conditions be zero. Suppose that $T(s)$ is a $(m\times k)$ matrix of functions such that

Then $T(s)$ is called the transfer function of the linear system.

Let $T$ be a matrix of complex rational functions. Then there exists a MIMO linear system $\mathrm{\Sigma }$, possibly with feedback, composed of taps, matrix amplifiers, summing junctions, differentiators and integrators such that the transfer function of $\mathrm{\Sigma }$ is $T$.