  We revisit and extend the Riccati theory, unifying continuous-time
linear-quadratic optimal permanent and sampled-data control problems, in finite
and infinite time horizons. In a nutshell, we prove that:-- when the time
horizon T tends to $+\infty$, one passes from the Sampled-Data Difference
Riccati Equation (SD-DRE) to the Sampled-Data Algebraic Riccati Equation
(SD-ARE), and from the Permanent Differential Riccati Equation (P-DRE) to the
Permanent Algebraic Riccati Equation (P-ARE);-- when the maximal step of the
time partition $\Delta$ tends to $0$, one passes from (SD-DRE) to (P-DRE), and
from (SD-ARE) to (P-ARE).Our notations and analysis provide a unified framework
in order to settle all corresponding results.
