Abstract
In this paper we consider an H∞ Kalman filtering problem for linear weakly coupled stochastic systems composed of N subsystems. The H∞ Kalman Filter is a robust optimal filter which eliminates the effects of a bounded noise and a variation of system parameters. To solve the Kalman filtering problem we use the Hamiltonian approach, which introduces the transformation for the exact closed-loop decomposition of the H∞ Kalman filtering Hamiltonian system. Using the proposed method, we can obtain N reduced-order Hamiltonian subsystems. In addition, we obtained the exact solution of the algebraic Riccati equations in terms of the solutions of the corresponding reduced-order subsystem algebraic Riccati equations. The introduced transformation produces a lot of savings especially for on-line computation since it allows parallel processing of information with lower-order Kalman filters.
