Abstract
The problem of the performance deterioration in an optimal regulator which is caused by the introduction of a Kalman filter as a state estimator is investigated. In this paper, time-invariant Kalman filters are used as state estimators for deterministic linear time-invariant systems like Luenberger observers, so that it is assumed that the gain matrix K of the filter can be chosen arbitrarily.
It is shown that there exist a positive constant ρ and a class of initial error-differencs, e(0), which are independent of the choice of filter gain matrices, such that performance deterioration, ΔJ, is bounded away from zero as shown by the form ΔJ≥ρ||e(0)||2unless the optimal feedback control law can be implemented by direct output feedback.
