Euler's discretization effect on a twisting algorithm based sliding mode control

In this paper, the Euler's discretization of the second order sliding mode control system with the twisting algorithm is studied. It shows that, for all values of discretization steps, initial conditions and allowable parameter setting, the system trajectories are always bounded. It also shows that for the uncertain systems, under a mild condition, the system trajectories are also bounded. Further, the periodic behaviors and limit cycles of the system trajectories are explored with conditions for the existence of periodic orbits formulated. Extensive simulation examples are given to show typical trajectories, and comparison between the first order and second order sliding mode control systems.