Difference and differential Riccati equations: a note on the convergence to the strong solution

The convergence of the solutions of the differential difference Riccati equations to the strong solution of the corresponding algebraic Riccati equation (ARE) is addressed. Detectability only is required in the analysis, and no assumption is made on the eigenvalues on the real imaginary axis (on the unit circle, in the discrete-time case). In particular, from the results, it follows that under the sole assumption of detectability, a positive definite initial condition guarantees convergence to the strong solution, even in the presence of unreachable eigenvalues on the imaginary axis or on the unit circle