Stability of dynamical polysystems via families of Liapunov functions

In this paper we deal with the problem of stability and asymptotic stability of critical points of dynamical polysystems. We obtain results concerning polysystems with and without constraints, by means of uniform families of Liapunov functions. Dynamical polysystems may be interpreted as the topological counterpart of switched systems: our results are compared to those previously obtained in the literature.