This paper presents new controller design conditions based on a parameter-dependent Lyapunov function for the polar coordinate fuzzy systems which were proposed in our previous papers. In the previous papers, we considered stability conditions and controller design conditions based on the so-called common quadratic Lyapunov function for the systems. In this paper, we utilize the descriptor system representation for the polar coordinate fuzzy system and the corresponding controller, and we derive the stabilizability conditions based on the parameter-dependent Lyapunov function to determine the feedback gains in the controller. The conditions are given in terms of LMIs