The singular linear-quadratic regulator problem and the Goh-Riccati equation

Feedback control for the singular linear-quadratic regulator problem is studied by means of several quite different techniques but from the single perspective of the Goh-Riccati equation. The equation is a variant of the standard Riccati equation which follows from applying Goh´s transformation to the singular problem to obtain a nonsingular problem. The Goh-Riccati equation is derived by means of four distinct methods, namely, Goh´s transformation, perturbation methods, generalized Legendre-Clebsch conditions, and fixed-structure optimization