A finite time convergent variable structure guidance law

For interception of maneuvering targets, mathematically speaking, the guidance laws based on traditional Lyapunov stability theory can only nullify the line of sight angular rate when time approaches infinity. Based on finite time stability theory of nonlinear control systems, a sufficient condition of finite time convergence of guidance system is given and a concise finite time convergent variable structure guidance law is proposed. Assume the relative velocity between the target and the missile is approximately constant. For intercepting the maneuvering target, the guidance law can ensure that the line of sight angular rate converge to zero before the final time of interception. The finite time convergence property by the guidance law is verified by simulation.