The implicit discretization of the super-twisting sliding-mode control algorithm

This paper deals with the analysis of the time-discretization of the super-twisting algorithm, with an implicit Euler method. It is shown that the discretized system is well-posed (in the sense that the control input is uniquely computable from known data and measured variable). The existence of a Lyapunov function with convex level sets is proved for the continuous-time closed-loop system. Then the global asymptotic Lyapunov stability of the unperturbed discrete-time closed-loop system is proved. The convergence to the origin in a finite number of steps is proved also in the unperturbed case. Numerical simulations demonstrate the superiority of the implicit method with respect to an explicit discretization with significant chattering reduction.