No necessary and sufficient condition for reachability of switched linear singular systems has been found, exceptuating the case of the so-called “equisingular systems”. Such a condition is not valid in the general case, as examples show.
Clotet, J., Magret, M. D. Some considerations about reachability of switched linear singular systems. "Far east journal of applied mathematics", 30 Novembre 2015, vol. 93, núm. 3, p. 179-190.