A generalized eigenproblem approach to singular control problems. I. LQG problems

Summarizes new results which give a general descriptor representation for the solution to the LQG (linear quadratic Gaussian) control problem. The descriptor representation applies without additional complexity to singular cases, i.e. when the associated noise intensities and/or control weightings are not invertible improper solutions. The authors also determine the limiting transfer function and resulting cost. The results reflect the reduction in dimension in the optimal feedback solution which can occur in the singular case. The results are based on an eigenspace solution to the cheap control problem obtained by the application of a known result on the invariant subspaces of analytic matrix functions of a single variable. The results also have significance to the LQG-LTR (loop transfer recovery) design procedure because they allow direct computation of the limiting controller which achieves LTR without the usual iteration