On subspaces associated with partial reconstruction of state vectors, the structure algorithm, and the predictable directions of Riccati equations

The close relations are discussed that exist among the three subspaces that arise in three apparently unrelated problem areas: 1) the subspace associated with the error of state vector reconstruction in informationally decentralized control problems; 2) the subspace associated with the solution of the Riccati equation; and 3) the null space of the certain observation matrix constructed by the structure algorithm.