<p>This paper proposes three new techniques and applies them to the performance analysis of T-S fuzzy system (TSFS) subject to two additive time delays: a five-parameters binary quadratic function negative-determination (five-parameters-BQFND) lemma, a Lyapunov-Krasovskii Functional (LKF) lemma and a genetic algorithm. First, a new quadratic function negative-determination lemma with five parameters is constructed. The introduction of these five parameters enhances the accuracy of the linear matrix inequality (LMI) estimation. The lemma is specifically designed for binary time-delay systems and can be applied to handle two types of time-delay square terms. Second, a new relaxed LKF lemma is proposed. The newly introduced LKF includes several free matrices. Despite the correlation among the vectors, the positive definiteness of the LKF is still guaranteed. Compared with previous studies, the free matrices are directly incorporated into the LKF rather than being introduced during the LMI estimation, which directly benefits the system performance analysis. Third, a genetic algorithm is introduced to optimize the five parameters of the new five-parameters-BQFND lemma. The algorithm allows for the optimization of these parameters, thereby improving system performance. Finally, the three new techniques are applied to the performance analysis of T-S fuzzy systems subject to two additive time delays, resulting in corresponding performance criteria. Simulation experiments validate the effectiveness of the proposed methods.</p>