Controllability of time-invariant singular linear systems

We consider triples of matrices (E;A;B), representing singular linear time invariant systems in the form E _ x(t) = Ax(t) + Bu(t), with E;A 2 Mn(C) and B 2 Mn£m(C), under proportional and derivative feedback. Structural invariants under equivalence relation characterizing singular linear systems are used to obtain conditions for controllability of the systems.