Simplified algebraic characterization of optimal singular control for autonomous linear plants

In an earlier publication[1] the authors extended the results of Wonham and Johnson[2] by characterizing the nature of the (stable) singular strip for a given performance index without recourse to a special transformation to phase coordinates. The solution presented there[1] required solving a (quadratic) matrix Riccati equation; whereas here the singular strip and the corresponding stable optimal feedback control law are found by factoring a polynomial which is computationally much easier to accomplish. The final result is illustrated by a numerical example.