[From Rick Marken (960113.1100)]
Bruce Abbott (950113.1125 EST) --
I think we are talking about different circumstances [re: gain and
the stability of a positive feedback system]
Yes, we are talking about different circumstances. I aim talking
about a closed loop system. You, as usual, are talking about an
open loop system (using closed loop terminology).
The gain, g, you are talking about is not _loop_ gain; it
is the linear operator in an open loop sequential process:
X(n) < g*X(n-1)
In this equation, g is not _loop_ gain; it is the degree to
which a variable changes state during discrete time intervals
So your discussion of gain has nothing at all to do which the
effect of _loop_ gain on the stability of a positive feedback
loop.
What do you suppose your leaky integrator is doing to the loop gain
on each iteration?
Nothing.
When you find the right answer to that question, you will know
why this positive feedback loop stabilizes.
Oh, thank you, wise one. I am not worthy.
But tell me, wise one, why you don't answer my questions about
Killeen's model. Are they so far beneath your incredible
inteelect that they do not merit even a dismissive smirk? Please,
oh master of control theory, tell me: are these questions of
mine not worthy of your consideration:
what is the controlled perceptual variable in the Killeen model? Did
Killeen test to see whether this variable is actually under control?
Why don't we apply the Killeen model to a situation where it is
easy to test whether or not the variable controlled by the model
is actually under control?
Best
Rick