Function space null controllability of linear delay systems with limited power

Abstract It is shown that if the system x (t) = L(t, x t ) + B(t) u(t), ∗ is null-controllable with square integrable controls, and if the system x (t) = L(t, x t ) is uniformly asymptotically stable, then the control system is null controllable with square integrable controls which lie in a closed unit ball with zero in its interior. This extends known results, and it is useful in the time optimal control problem of delay equations.