Analytical Solution for Finite-Time Convergence Analysis of Higher Order Terminal Sliding Mode Manifold

This paper examines the finite-time convergence characteristics of higher order terminal sliding manifold for control design purposes. Here, with a set of conditions to be satisfied, a unique analytical solution for this particular type of nonlinear higher order differential equation is obtained. As a result, the convergence time is then calculated accordingly and the finite-time converging-to-zero trajectories of the states, when the sliding mode is reached, can be systematically designed.