Capturability of a Sliding-Mode Guidance Law With Finite-Time Convergence

Using the Lyapunov-like approach, the capturability of a recently proposed sliding-mode guidance law, which is used for exoatmospheric interception and can guide the line-of-sight (LOS) angular rate to converge to zero or its small neighborhood in a finite time, is thoroughly analyzed. The target is assumed to have an arbitrary but upper-bounded maneuvering acceleration. A more realistic definition of capture is considered. The upper bound of the commanded acceleration is obtained and so is the capture region. The new theoretical findings are extended to the three-dimensional space with the help of the rotating LOS coordinate system.