where S is the solution of the corr

where S is the solution of the corresponding ARE.
In general, the plant states are not measurable and
so have to be estimated. The traditional choice would
be the Kalman estimator, but the effective application
of such an estimator requires some a priori information
on the noise characteristics, which is, in general, not
known. Hence, a deterministic state observer (Dorf
and Bishop, 2008) is used. This observer can be related
to the Kalman estimator and has an interpretation in
the LQG framework, as is shown subsequently. One of
the benefits of the traditional estimator is the possibility
to specify the weighting matrices for the relative estimation
error in a more natural and transparent way.
This serves the purpose of this particular control design
well, as it is desired that the closed-loop properties can
be adjusted in a deterministic way. The optimal observer
is such that it minimizes the cost function