The exact slow-fast decomposition of the algebraic riccati equation of singularly perturbed systems

The algebraic Riccati equation of singularly perturbed control systems is completely and exactly decomposed into two reduced-order algebraic Riccati equations corresponding to the slow and fast time scales. The pure-slow and pure-fast algebraic Riccati equations are nonsymmetric ones, but their O(ϵ) perturbations are symmetric. It is shown that the Newton method is very efficient for solving the obtained nonsymmetric algebraic Riccati equations. The presented method is very suitable for parallel computations. In addition, due to complete and exact decomposition of the Riccati equation, this procedure might produce a new insight in the two-time scale optimal filtering and control problems.