Optimal Control and Filtering of Weakly Coupled Linear Discrete Stochastic Systems by The Eigenvector Approach

-In this paper the regulator and filter algebraic Riccati equations, corresponding to the steady state optimal control and filtering of weakly coupled linear discrete stochastic systems are solved in terms of reduced-order sub problems by using the eigenvector approach. The eigenvector method outperforms iterative methods (fixed point iterations, Newton method) of solutions to reduced-order sub problems in case of higher level of coupling between subsystems. In such cases the iterative methods could fail to produce solutions of the corresponding algebraic Riccati equations.