A theorem on neutral delay systems (Q1062950)

The author considers neutral delay equations with finitely many discrete non-commensurable delays. As is well known, the eigenvalues s of such an equation are asymptotically (as Im \(s\to \infty)\) determined by the eigenvalues of the difference part of the equation. These eigenvalues can be shifted only via derivative feedback. ''Formal stabilizability'' (implying in particular stabilizability independent of the delays) of the difference part is characterized via a controllability property using algebraic methods. The result generalizes a theorem known for commensurable delays.