  When implementing a non-continuous controller for a cyber-physical system, it
may happen that the evolution of the closed-loop system is not anymore
piecewise differentiable along the trajectory, mainly due to conditional
statements inside the controller. This may lead to some unwanted chattering
effects than may damage the system. This behavior is difficult to observe even
in simulation. In this paper, we propose an interval approach to characterize
the sliding surface which corresponds to the set of all states such that the
state trajectory may jump indefinitely between two distinct behaviors. We show
that the recent notion of thick sets will allows us to compute efficiently an
outer approximation of the sliding surface of a given class of hybrid system
taking into account all set-membership uncertainties. An application to the
verification of the controller of a child swing is considered to illustrate the
principle of the approach.
