Near-optimal output feedback regulation of ill-conditioned linear systems

Issues pertaining to the well-posedness of a two time scale approach to the optimal output feedback regulator problem are examined. An approximate quadratic performance index is derived, reflecting a two time scale decomposition of the system dynamics. It is shown that, under mild assumptions, minimization of this cost leads to feedback gains providing a second-order approximation of the full system optimal performance. This is verified with a numerical example. A convergent sequential numerical algorithm for calculating these gains is described.