Continuous second-order sliding mode control: Convergence time estimation

The contribution of this paper is threefold. First, a vector super-twisting algorithm is designed to provide a direct extension of the conventional scalar supertwisting control, without any additional terms. An upper estimate of its convergence time is calculated. Second, a fixed time convergent continuous vector super-twisting-like algorithm is presented and its fixed convergence time is estimated. Third, an estimate of the finite convergence time of the scalar supertwisting algorithm is obtained as a particular case of the vector super-twisting one, which occurs to be less conservative than the one derived specially for the scalar case. The proposed theory is applied to F-16 jet-fighter flight control.