摘要：＂Dynamic extension＂ is commonly used for stabilization of the planar vertical take off and landing （PVTOL） system. Most controllers designed by the method are based on ＂dynamic＂ control Lyapunov functions （CLFs）. We design a C^∞ differentiable ＂static＂ CLF for the PVTOL system by dynamic extension and minimum projection method. Then we propose an inverse optimal controller based on the static CLF that attains a gain margin. We design an adaptive control input and show the robustness of the controller by computer simulation.