The author considers piecewise continuous dynamical systems, so-called switch systems, modelled by the following autonomous initial value problem, that is
where , and are vector-valued functions, and denotes the th canonical unit vector in . One of the first goal of the author is to present the assumptions which provide, that (1) defines a dynamical systems. The second purpose is to explore the possibility to synchronize two such switch dynamical systems with chaotic motion. To this end the author uses the Filippov regularization.