This paper deals with Takagi-Sugeno (T-S) systems stabilization based on dynamic output feedback compensators (DOFC). In fact, only few results consider DOFC for T-S systems and most of them propose quadratic Lyapunov functions to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and to enhance the closed-loop transient response, we provide for T-S uncertain closed-loop systems non-quadratic stability conditions. Based on a fuzzy Lyapunov candidate function and the descriptor redundancy property, these stability conditions are written in terms of linear matrix inequalities (LMI). Afterward, the DOFC is designed with H∞ criterion in order to minimize the influence of external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approaches.