DIFFERENCE AND DIFFERENTIAL RICCATI-EQUATIONS - A NOTE ON THE CONVERGENCE TO THE STRONG SOLUTION

This note deals with the convergence of the solutions of the differential and difference Riccati equations to the strong solution of the corresponding ARE. 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 our result, 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.