This brief concerns a new digital redesign (DR) technique for an observer-based output-feedback control (OBOFC) system. The term DR involves converting an analog controller into an equivalent digital one in the sense of state-matching. The considered DR problem is viewed as a convex minimization problem of the norm distances between linear operators to be matched and its constructive condition is formulated in terms of linear matrix inequalities (LMIs). The main features of the proposed method are that the state estimation error in the plant dynamics is considered for the state-matching condition that was ignored in the earlier works; the stability is guaranteed within the redesign procedure; the separation principle on the DR of the OBOFC is explicitly shown. A numerical example is included for visualizing the feasibility of the proposed technique.