In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback $H_{infty}$ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback $H_{infty}$ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better $H_{infty}$ performance. The effectiveness of the proposed approach is shown through two numerical examples.