This paper investigates robust observer based H(infinity )control problem for uncertain discret-time Takagi-Sugeno fuzzy systems. By using fuzzy Lyapunov functions and some special derivations, Sufficient relaxed conditions for synthesis of a fuzzy observer and a fuzzy controller for T-S fuzzy systems are derived in terms of a set of linear matrix inequalities (LMIs) which can be solved using a single-step procedure. The proposed approach provides more relaxed conditions comparing with the existing techniques in literature which use a quadratic Lyapunov function and the so-called two-step procedure, also ensures better H(infinity )control performance. Simulation example is presented to show the effectiveness of the proposed design method. Copyright (C) 2020 The Authors.