Final value theorem conditions

1. When can you apply final value theorem?
2. Which of the following conditions must hold while applying the final value theorem?
3. Can final value theorem be applied to unstable system?
4. Which of the following conditions are necessary for the validity of initial value theorem?

When can you apply final value theorem?

The Final Value Theorem (in Control): If all poles of sY(s) are strictly stable or lie in the open left half-plane (OLHP), i.e., have Re(s)<0, then y(∞)=lims→0sY(s).

Which of the following conditions must hold while applying the final value theorem?

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

Can final value theorem be applied to unstable system?

Note that we can only use the Final Value Theorem if a system is stable, or at least has all its poles at the origin (and the left half plane).

Which of the following conditions are necessary for the validity of initial value theorem?

Conditions for the existence of Initial value theorem

The function f(t) and its derivative f(t) should be Laplace transformable. If time t approaches to (0⁺) then the function f(t) should exists.