119 BIBO stability in terms of eigenvalues of $A$

Suppose that all eigenvalues ${\lambda }_j$ of $A$ satisfy , and that $U$ is bounded on $(0,\mathrm{\infty })$. Then all solutions to

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

$$Y=CX+DU$$

are bounded on $(0,\mathrm{\infty })$. Hence $(A,B,C,D)$ is BIBO stable.