114 BIBO stability

Let $(A,B,C,D)$ be a linear system

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

$$Y=CX+Du$$

such that for all bounded inputs $u(t)$ for $t\in (0,\mathrm{\infty })$, all outputs $y$ are bounded for $t\in (0,\mathrm{\infty })$. Then we say that the system is bounded-input bounded-output stable, or BIBO stable.