Finite-time stabilization of uncertain triple integrator with only switch and gain

This paper presents a twisting like control algorithm for finite-time stabilization of triple integrator, thus providing an algorithm for sliding mode control of order three. The algorithm needs only signs of the switching function and its derivatives. The gains in the algorithm follow simple inequalities to give finite-time convergence of σ, σ̇ and σ̈. Also, the conditions are derived for the uncertain double and triple integrators.