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Contents
1 Introduction to Final Value Theorem^{[1]}
The Final Value Theorem allows the evaluation of the steadystate value of a time function from its Laplace transform. The final value theorem is only valid if is stable (all poles are in th left half plane). If all poles are in the left half plane then
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2 Continuous Time Final Value Theorem^{[2]}
3.26 
2.1 Proof
Consider when and rewrite as
Then
Result 1 
Partial fractions can be used to see this another way
If and all other then becomes the steadystate value of and
Result 2 
As you can see Result 1 is the same as Result 2.
2.2 Example
2.2.1 The Right Way
Find the steadystate value of the system
Applying the final value theorem:
2.2.2 The Wrong Way
Find the final value of the signal
Answer:
However,
Remember that the final value theorem is only valid when all the poles are in the left half plane (). Clearly this system has a pole at +2 and therefore the final value theorem does not apply.
3 DiscreteTime Final Value Theorem
4 References
 Franklin, G. F., EmamiNaeini, A., and Powell, J. D. 1993 Feedback Control of Dynamic Systems. 3rd. AddisonWesley Longman Publishing Co., Inc. ISBN 0201527472