Asymptotic Expansions of Singularly Perturbed Chandrasekear Type of Equations

The singular perturbation theory provides a powerful design and analysis approach for model order reduction. Another method of simplifying the calculation of feedback gains in a LQG problem is the Chandrasekhar algorithm, which replaces the usual Riccati approach. The method presented in this paper combines the advantages inherent in the singular perturbation theory with those of the Chandrasekhar algorithm. This is accomplished after an asymptotic power series solution is constructed and analyzed. Then, the terms of the asymptotic series can be computed via a simpler way, since they involve the solution of lover dimensional sub-problems of the Chandrasekhar type.