Minimax observation problems for linear descriptor difference equations

The sufficient condition for existence of linear function's ∑ N+1K=0(lk ∣ xk)Rn minimax estimations is obtained on the basis of observations yk = Hkxk + η k up to N moment assuming that lk &n; Rn, xk is a solution of the linear descriptor difference equation Fk+1xk+1 − Ckxk = fk, F0x0 = g0, k = 0, N, g0, fk - are some unknown vectors from the set G, η k - is random vector with unknown correlation matrix Rk which belongs to set G2. It is shown that in case of quadric sets G, G2 the unique minimax estimation exists and can be represented in terms of solutions of some linear descriptor equations systems.