This paper considers the stable and quadratic finite-horizon optimal design problem of the fuzzy parallel-distributed-compensation (PDC) controllers for the Takagi-Sugeno (TS) fuzzy-model-based control systems by integrating the stabilizability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), where the stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algorithm only involving the algebraic computation is derived in this paper for solving the TS-fuzzy-modelbased feedback dynamic equations, and then is integrated with both the proposed sufficient LMI condition and the HTGA to design the stable and quadratic optimal fuzzy PDC controllers of the TSfuzzy- model-based control systems under the criterion of minimizing a quadratic integral performance index.