  The sliding mode approach is recognized as an efficient tool for treating the
chattering behavior in hybrid systems. However, the amplitude of chattering, by
its nature, is proportional to magnitude of discontinuous control. A possible
scenario is that the solution trajectories may successively enter and exit as
well as slide on switching mani-folds of different dimensions. Naturally, this
arises in dynamical systems and control applications whenever there are
multiple discontinuous control variables. The main contribution of this paper
is to provide a robust computational framework for the most general way to
extend a flow map on the intersection of p intersected (n--1)-dimensional
switching manifolds in at least p dimensions. We explore a new formulation to
which we can define unique solutions for such particular behavior in hybrid
systems and investigate its efficient computation/simulation. We illustrate the
concepts with examples throughout the paper.
