Generalization of the twisting convergence conditions to non-affine systems

The twisting algorithm is a second order sliding mode technique for which convergence conditions have been established. However, these conditions are limited to systems that are affine in the control. In this paper, new convergence conditions that are not limited to such systems, are proposed. Furthermore, it is shown that in the affine case, state-of-the-art convergence conditions are more conservative than the new conditions. Two examples illustrate the difference of conservatism and the way that the new conditions ensure the convergence of systems non-affine in the control input.