The classical problem of the sliding mode control design, which guarantees finite-time reaching and further system motion on a linear hyperplane, is considered for the linear time-invariant disturbed system with the noised measurements of the output. The control law, which provides to the closed-loop system the optimal reaching (as close as possible) of the selected sliding surface, is designed using minimax state observer. The case of discontinuous and continuous admissible feedbacks are studied. The theoretical results are supported by numerical simulations.