Lyapunov Stability Analysis of the Implicit Discrete-Time Twisting Control Algorithm

An implicit discrete-time version of the twisting sliding-mode control algorithm is considered. The framework of variational inequalities is used to define the control input values. This provides the foundation for both the analysis of the controller and the numerical computations. The controller is shown to be well-defined and the discrete-time closed-loop system's fixed point is finite-time globally stable in the sense of Lyapunov. The analysis is led in the unperturbed case, and numerical simulations demonstrate the efficiency of the proposed controller when a disturbance acts on the system.