Divergence theorem for super twisting control

As follows from analysis of stability for super twisting sliding mode control [1], for any bounded disturbance the controller parameters exist such that the state converges to the origin in the system state plane. The minimal possible convergence time is dictated by the necessary conditions. The question discussed in this paper: can the set of parameters be found such that convergence takes place for an arbitrary disturbance? The answer is negative: for any set of the controller parameters there exists a bounded disturbance such that the state trajectories are diverging. It means that the controller parameters should be tended to infinity to stabilize the system with increasing disturbances. As a result chattering suppression property of the super twisting control is essentially degraded even if compared with the conventional first order sliding mode control.