**Final value theorem**

** **The final value theorem is used to trace out the final signal value using the signal spectrum.

**Laplace final value theorem**

If you know F(s), and if you don’t know F (t) related to that F(s), you can trace the final value of that F (t).

The F (t) and its 1^{st} derivate are replacing transformable, then the find value of F (t) is

** F (∞) = Limit. sf. (s) **

** s→0**

**Final value theorem steady-state error**

It is a deviation of the steady state is known as steady state error. We can find the steady state error using the final value theorem, it is represented with **ess.**

**ess=limt→∞e(t)=lims→0sE(s)ess=limt→∞e(t)=lims→0sE(s)**

Where,

E(s) is the Laplace transform of the error signal, **e(t)e(t)**

**Initial and final value theorem**

The initial theorem is used to trace initial value using known spectrum and unknown it is,

** F (0) = Limit sf (s)/ s→∞**

The final theorem is used to trace the final value using spectrum and signal it is like using,

** F (∞) = Limit. Sf. (s)/ s→0**

Using both the theorems such as initial and final theorems, you can easily trace the overall range of the signal.