Linear Systems with Prescribed Similarity Structural Invariants

The problem of the existence of linear systems $\dot{x}(t)=Ax(t)+Bu(t)$ with prescribed structural invariants for system similarity is studied. Namely, we solve the problem of the existence of such a system with prescribed controllability indices, Hermite indices, and invariant factors when the invariant factors of A (which are also invariants under system similarity) are given.