  We provide a rigorous solution to the problem of constructing a structural
evolution for a network of coupled identical dynamical units that switches
between specified topologies without constraints on their structure. The
evolution of the structure is determined indirectly, from a carefully built
transformation of the eigenvector matrices of the coupling Laplacians, which
are guaranteed to change smoothly in time. In turn, this allows to extend the
Master Stability Function formalism, which can be used to assess the stability
of a synchronized state. This approach is independent from the particular
topologies that the network visits, and is not restricted to commuting
structures. Also, it does not depend on the time scale of the evolution, which
can be faster than, comparable to, or even secular with respect to the the
dynamics of the units.
