  In this paper, an eigenvalue mapping-based discretization method is applied
to discretize the generalized super-twisting algorithm. The existing eigenvalue
mapping is extended to the complex domain which greatly enlarges the range of
parameter selection. Furthermore, we present the clue to find new eigenvalue
mapping functions (EMFs). One new hybrid EMF and three brand-new EMFs are
proposed in this paper. In contrast to the conventional methods, the proposed
discretization method totally avoids the discretization chattering and the
control precision is enhanced in terms of the steady-state error. Besides, the
control precision is insensitive to the overestimation of the control gains,
which benefits the gain tuning of the controller in practice. Simulation
examples verify the effectiveness and superiority of the proposed
discretization methodology.
