The solution of the Riccati differential equation is reported to be asymptotically close to the solution of the projection Riccati differential equation (PRDE). The asymptotic behavior of the latter is analyzed on an explicit formula. The almost periodic asymptote of the solution of the PRDE is computed by an algorithm based upon the concepts of aperiodic- almost-periodic generator decomposition of a linear map, and row-staircase form of a polynomial matrix. The analysis provides ultimately a convergence criterion.
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