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.

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