I thought that the solution posted in the Bonus 3 for problem 4 is slightly wrong in explaining why System II is Stable.

Its given that $x(t) \le B$

$y(t) = x(t) * h(t) = \int_{-\infty}^{\infty} x(\tau - t)h(\tau)\, d\tau$

$\Rightarrow ~y(t) \le \int_{-\infty}^{\infty} Bh(\tau)\, d\tau ~~~\leftrightarrow~~~x(\tau - t)~is~stable~as~x(t)~is~stable.$

$\Rightarrow ~y(t) \le B\int_{-\infty}^{\infty} e^\tau[u(\tau-2) - u(\tau-5)]\, d\tau$

$\Rightarrow ~y(t) \le B\int_{2}^{5} e^\tau\, d\tau$

$\Rightarrow ~y(t) \le B(e^5 - e^2)$

Hence $y(t) \le Bc \le C~, ~~~ (where~c = e^5 - e^2 ~and ~~C = B*c)$

$\therefore y(t) ~is ~bounded$

## Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett