It seems like highly specialized jargon that's probably defined
somewhere in the text you got the phrase from. Maybe you can get it from
context, or get help from someone if you supply the context.
What is "output feedback"? One usually feeds back from output to input.
Engineering is the art of making what you want from things you can get.
I didn't find any explanation in the textbook including "index" at the
end of the book. Instead, I find a paper which said that "static
output feedback" is an ordinary feedback gain such as L (a matrix or
something) while "dynamic output feedback" is a system(state space or
something, like an observer).
I think that static output feedback includes feedback signal
response all the way down in frequency to steady state (DC),
while dynamic output feedback includes a high pass function
that rolls off the feedback response as frequency falls
below some cut off frequency, so results in no feedback in
the steady state case.
I didn't know the terms so I briefly browsed google and got two
1. Static feedback is normal state feedback. Dynamic feedback
includes integral of error.
2. Static feedback is a constant feedback gain. Dynamic feedback is
a feedback gain that is a function of frequency.
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