An invariant parameter in linear estimation and control

An invariant parameter for the joint observer-controller design, the forward and backward Kalman-Bucy (KB) filter, and the LQG control problem is obtained. Next the balancedness in balanced realizations is interpreted from the invariant parameter viewpoint. It is shown that in general a balanced realization does not lead to a balanced observer-controller design. Also the concept of continuous-time balanced stochastic realization is developed.