Minimax observation problems for singular linear difference equations

The minimax estimations of the scalar product ⟨l, x(N)⟩ are obtained on the basis of observations y(k) = H(k)x(k) + η(k) up to N − 1 moment assuming that l ∈ L ⊆ Rn, x(k) is a solution of the difference equation S(k + 1)x(k + 1) = A(k)x(k) + f(k), x(0) = f0 with some rectangular matrix S(k) of rank p(k), f0, f(k) – are unknown vectors, η(k) – is random vector with unknown correlation matrix R(k), M η(k) ≡ 0.