An observer is a dynamical system with input (u,y) and output, say which asymptotically estimates the state x, i.e., for all initial states and
for every input.
An
observer exists iff (C,A) is detectable. Further,
if (C,A) is detectable, then a full
order Luenberger observer is given by
where L is a matrix such that A+LC is stable.
Observer-based controller:
and