  We investigate the task of controlling ensembles of initial and terminal
state vectors of parameter-dependent linear systems by applying
parameter-independent open loop controls. Necessary, as well as sufficient,
conditions for ensemble controllability are established, using tools from
complex approximation theory. For real analytic families of linear systems it
is shown that ensemble controllability holds only for systems with at most two
independent parameters. We apply the results to networks of linear systems and
address the question of open-loop robust synchronization.
