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

The algebraic Riccati equation for 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 asymmetric ones, but their O(ε) perturbations are symmetric. It is shown that the Newton method is very efficient for solving the obtained asymmetric algebraic Riccati equations. The method presented is very suitable for parallel computations. Due to the complete and exact decomposition of the Riccati equation, this procedure might produce new insight into the two-time-scale optimal filtering and control problems