Incremental stability of planar Filippov systems

We study the problem of proving incremental stability of a planar Filippov system. In particular, referring to systems that present an attractive sliding region on their discontinuity boundary, we will give a differential condition on such region able to guarantee incremental exponential stability of sliding mode trajectories. We will then derive conditions for the incremental stability of the whole system. The approach is based on using tools from contraction theory, extending their applicability to include discontinuous dynamical systems.