The problem of the existence of linear systems (x) over dot (t) = Ax (t) Bu (t) with prescribed structural invariants for system similarity is studi
ed. Namely, we solve the problem of the existence of such a system with pre
scribed controllability indices, Hermite indices, and invariant factors whe
n the invariant factors of A (which are also invariants under system simila
rity) are given.