Synchronization of networked piecewise smooth systems

This paper is concerned with the synchronization of networks of switching dynamical systems. In particular, conditions are derived for all nodes in a network of such systems to converge towards a common synchronous evolution. The key assumption is for the vector field to be in a suitable form that we call QUAD affine. Under this assumption, we show that the network of interest synchronizes even if the vector field is discontinuous and sliding motion is possible. The theoretical results are complemented by numerical simulations on a testbed example.