  The purpose of this paper is to investigate the role that the continuous-time
generalised Riccati equation plays within the context of singular
linear-quadratic optimal control. This equation has been defined following the
analogy with the discrete-time generalised Riccati equation, but, differently
from the discrete case, to date the importance of this equation in the context
of optimal control is yet to be understood. This note addresses this point. We
show in particular that when the continuous-time generalised Riccati equation
admits a symmetric solution, the corresponding linear-quadratic (LQ) problem
admits an impulse-free optimal control.
