This paper presents a new approach for the stability analysis and controller synthesis of discrete-time Takagi-Sugeno fuzzy dynamic systems. In this paper, nonmonotonic Lyapunov function is utilized to relax the monotonic requirement of Lyapunov theorem which renders larger class of functions to provide stability. To this end, three new sufficient conditions are proposed to establish global asymptotic stability. In this regard, the Lyapunov function decreases every few steps; however, it can be increased locally. Moreover, a new method is proposed to design the state feedback controller. It is shown that the Lyapunov function and the state feedback control law can be obtained by solving a set of Linear Matrix Inequalities (LMI) or Iterative Linear Matrix Inequalities (ILMI) which are numerically feasible with commercially available softwares. Finally, the exhausted numerical examples manifest the effectiveness of our proposed approach and that it is less conservative compared with the available schemes.