Multivariable continuous fixed‐time second‐order sliding mode control: design and convergence time estimation

The contribution of this study is threefold. First, a vector (multivariable) super‐twisting algorithm is designed to provide a direct extension of the conventional scalar super‐twisting control, without any additional terms. An upper estimate of its convergence (settling) 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 super‐twisting 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 theoretical concepts are illustrated in a number of scalar and multivariable examples.