| Line 10: | Line 10: | ||
<math> \Rightarrow ~y(t) \le B\int_{2}^{5} e^t\, dt </math> | <math> \Rightarrow ~y(t) \le B\int_{2}^{5} e^t\, dt </math> | ||
| + | |||
| + | <math> \Rightarrow ~y(t) \le B*(e^5 - e^2) </math> | ||
Revision as of 12:00, 1 July 2008
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(t)h(t)\, dt $
$ \Rightarrow ~y(t) \le \int_{-\infty}^{\infty} Bh(t)\, dt $
$ \Rightarrow ~y(t) \le B\int_{-\infty}^{\infty} e^t[u(t-2) - u(t-5)]\, dt $
$ \Rightarrow ~y(t) \le B\int_{2}^{5} e^t\, dt $
$ \Rightarrow ~y(t) \le B*(e^5 - e^2) $
