On the reduction of the continuous-time generalized algebraic Riccati equation: An effective procedure for solving the singular LQ problem with smooth solutions

This paper presents a reduction technique for the continuous-time constrained generalized Riccati equation arising in the context of the singular Linear Quadratic (LQ) optimal control problem. This technique allows to express the solutions of the constrained generalized Riccati equation in terms of the solutions of a reduced-order standard Riccati equation. This result is used to provide a solution to the singular LQ problem with closed-loop stability in the case when the allowed controls are restricted to be regular for any initial condition.