92 Solving MIMO by Laplace transforms

Let $A,B,C,D$ be constant matrices, and suppose that the input function satisfies $(E)$. Then the output $Y$ of the linear system

$$\frac{dX}{dt}=AX+BU$$

$$Y=CX+DU$$

$$X(0)=0$$

in $(E)$ is uniquely determined, and the Laplace transform satisfies

$$\widehat{Y}(s)=T(s)\widehat{U}(s).$$