In relation to the

biological system, negative feedback has many

positive features. To take a very

simplified model:

|---------|
+ | K |
--->O---------->| ------ |------------------------->
I ^ | sT+1 | | O
-| |---------| |
| |
|---------------------------------|

Aside from being very

accurate, the negative feedback system also has a very

unintuitive feature. For example:

Our transfer function H = K/(sT+1), a simple

low pass filter. The transfer function for the loop would be
H = H/(1+H) which would if we subbed in the equations be:

{K/sT+1} / {1+K/(sT+1)}

which would simplify further to get

k/sT+1+k

The steady state gain (the gain at an unvarying input or s=0) would be come k/1+k.

Now, lets say in a normal person the

gain of the filter is 9. Then the gain of the entire loop would be 9/1+9 which would be 0.9. Now lets say you had a lesion in your brain which killed off about 4 neurons in this simplified case. Your gain would drop to 5. However, the loop gain would be 5/1+5 which is 0.83. Therefore, a

loss of 44% of the number of neurons involved in a

pathway would only leave you with a loss of 7.8% of system gain. Very

useful!

Of course this is all very

simplified. There are indeed no biological system in which you have a negative feedback with a single low pass filter. But it does give you a nice example of how they help the body

resist damage.