Multivariable Super-Twisting Algorithm for a class of systems with uncertain input matrix

In this paper, we propose a new design for a multivariable Super-Twisting Algorithm, which does not require the exact knowledge of the system input matrix. In addition, by means of a nonlinear (state-dependent) time scaling we propose a new algorithm with variable gains which is able to present global stability properties for wider class of nonlinear disturbances. The latter can be analysed using the same theoretical framework as in the case of constant gains. The theoretical results are illustrated by simulations.