Exact decomposition of the algebraic Riccati equations of deterministic and stochastic multimodeling optimal control and filtering problems

We show how to exactly decompose the algebraic Riccati equations of deterministic and stochastic multimodeling in terms of one pure-slow and two pure-fast algebraic Riccati equations. In addition, we show how to completely decompose the optimal Kalman filter of the multimodeling structures in terms of pure-slow and pure-fast well-defined reduced-order, independent Kalman filters.