Chang-Kyung Ryoo/ Yoon-Hwan Kim and Min-Jea Tahk
International Journal of Aeronautical and Space Sicences, vol. 7, no. 2, pp.1-13, 2006

Abstract : 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 point. 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. Physically, the equilibrium subspace denotes the direction of missile velocity to the target. By using a single Lyapunov function candidate, capturability of several PN laws for a stationary target is then proved for examples. In this approach, there is no assumption of the constant speed missile. The proposed method is expected to provide a unified and simplified scheme to prove the capturability of various kinds of guidance laws.

Keyword : Guidance, proportional navigation, capturability, Lyapunov stability