# Final Value Theorem

I had a question about the final value theorem:

lim sF(s)
S->0

=

lim F(t)
t->infinity

I was told I can only use this if I know that a final value exists for f, or in other words that f(infinity) exists.

How can I check if it exists? If I have F(s), the only way I can think to check is to find the inverse Laplace and then see. If I do that, then there is no use of me applying the final value theorem as I will already know what it is.

Can some explain how one can determine whether or not the final value exists before applying the theorem?

Thanks!!

## Answers and Replies

anyone?

Well, if you have the transfer function of a system, by analyzing the poles you can determine whether the system is a stable or an unstable one. Giving an appropriate input to a stable system results in an output response that converges to a particular value as t tends to infinity while for an unstable system the output goes to infinity (i.e. it is not bounded)

I think you USE the final value theorem to verify IF the time function converges to a real value. Basically you solve lim sF(s) for s->0, and if this value exists then the transfer function is good and works because lim sF(s) for s->0 = lim f(t) for t->infinity. If the transfer function is good you would get the same value when solving either limit(if you know the time function). The difference would be that solving lim sF(s) for s->0 is easier because many terms of the transfer function will cancel out because of the s->0.

Hope you got it!!