Discretisation of sliding mode based control schemes

The paper introduces an approach to discretization of non-linear control laws with a Lipschitz property. The sampling time is defined as a parameter which must be selected sufficiently small so that the closed loop system is stable. In contrast to similar results, the stabilizing effect of the control is taken into account. This can result in less conservative constraints on the minimum sampling frequency. The discretization techniques are explained on a general non-linear model and applied to the discretization of a non-linear, robust sliding-mode-like control law. Similar robustness features as for continuous control are demonstrated. Non-smooth Lyapunov functions are used for the discretized sliding-mode-like control introducing cone shaped regions of the state space. One of these cone shaped regions coincides with a cone shaped layer around the sliding mode defined by the continuous sliding-mode like control. A stability theorem using non-smooth Lyapunov functions is provided