Discrete-Time Twisting Algorithm Implementation With Implicit-Euler ZOH Discretization Method

The significant numerical chattering hinders control applications of the twisting algorithm in digital environments. Previous implicit discrete-time implementation algorithms have the potential to attenuate the numerical chattering, but they require numerical solvers or do not consider the zero-order hold (ZOH) effect of Analog to Digital Converter (ADC) devices in digital control applications. This brief introduces an enhanced implementation algorithm for the famous twisting algorithm with the ZOH discretization method. It entails no numerical solvers and takes the ZOH effect into account, which enables control applications of the twisting algorithm in practice. The stability properties of the proposed realization algorithm are also analyzed with Lyapunov methods. Comparing to the previous implicit-Euler based implementation scheme for the twisting algorithm, the proposed one significantly attenuates the chattering in the presence of the ZOH effect without the requirement of any numerical solver.