Exact-slow fast decomposition of the H∞ filtering Riccati equation of singularly perturbed systems

The H_∞ filtering Riccati equation, associated with filtering problem, of standard singularly perturbed systems is completely and exactly decomposed into two reduced-order H_∞ filtering Riccati equations corresponding to the slow and fast time scales. The pure-slow and pure-fast H_∞ filtering Riccati equations are nonsymmetric ones; however, their O(ε) perturbations are symmetric. It will be shown that the Newton method is very efficient for solving the obtained nonsymmetric H_∞ filtering Riccati equations. This method is suitable for parallel computations. Due to complete and exact decomposition of the Riccati equation, this procedure might produce new insight into the two-time scale H_∞ output feedback problem.