Abstract
In optimal regulator problems an increase in the value of the performance index (P.I.) is in general encountered when a Luenberger observer is employed to construct the estimates of the state-variables which are not available by direct measurement.
In this paper exp Dt (D: the coefficient matrix of observer) is studied with respect to the increase in P.I. and it is shown that for the case where n≥3 (n: dimension of the system), in almost all cases the increase in P.I. becomes arbitrarily large when the real parts of the observer eigenvalues become highly negative. Moreover it is discussed for what quadratic performance index the control law using the estimates of the state-variables is optimal. In this case, a sufficient condition is derived, and the relation between the weighting coefficients in the performance index and the eigenvalues of the observer is discussed.
