Incremental stability of bimodal Filippov systems in ℝn

We present an approach to study contraction of sliding mode solutions in n-dimensional Filippov systems and characterize global convergence of their trajectories towards each other. The results extend to n-dimensional systems with discontinuous right-hand sides the approach proposed in [1] for the planar case. Sufficient conditions for the incremental stability of the sliding vector field are derived using contraction theory. These are then complemented with conditions for global attractivity of the sliding region to prove global convergence of trajectories of the Filippov system of interest towards each other within a region of interest. The theoretical derivations are illustrated by means of a representative numerical example.