Consider the function , where F(s) is Laplace transform of function f(t). The initial value of f(t) is:

Initial value theorem:

The initial value of a function with a given Laplace transform can be obtained using the Initial value theorem as:

It is applicable only when the number of poles of C(s) is more than the number of zeros of C(s).

Application:

Since the number of poles is greater than the number of zeros, we can apply the initial value theorem as:

f(0) = 0

Final value theorem:

​The final value theorem states that the final value of a system can be calculated by

F(s) is the Laplace transform of the function.

For the final value theorem to be applicable, the system should be stable in steady-state and for that real part of poles should lie on the left side of s plane.