The Lyapunov stability theory has been known inadequate to prove capturability of guidance laws because the equations of motion resulted from the guidance laws do not have the equilibrium points. By introducing a proper transformation of the range state, the original equations of motion for a stationary target can be converted into nonlinear equations with a specified equilibrium subspace that denotes the direction of missile velocity to the target. Applying the single Lyapunov function candidate to several PN laws, we show that either the equilibrium subspace is asymptotically stable or the nonlinear system is ultimately bounded. In our approach, there is no assumption of the constant speed missile. The proposed method is expected to provide a unified and simple scheme to prove the capturability of various guidance laws. Nomenclature ,, mm m rV a G G G = position, velocity, and acceleration vector of the missile r G = relative range vector from the target to the missile c r = specified radius of the sphere surrounding the target 0 r = initial range from the target to the missile s = 2 () c rr − V = Lyapunov function candidate , LL ψθ = azimuth and elevation angle of the LOS to the inertial reference frame , mm ψθ = azimuth and elevation angle of the missile velocity to the LOS reference frame BR ω = barrel-roll frequency