Observers and
Observer-Based Controllers

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