Limited authority of actuators implies that real control signals are always constrained, and in almost all cases, this produces a degradation in the performance of the system. It is thus of practical importance to understand the fundamental aspects of this performance degradation. In this paper, we take an initial step by proposing a way to characterize the performance limitations that arise in closed-loop stable linear systems due to the constraints on the magnitude of the control signal. Specifically, we evaluate the cost associated with the constraints via the L2 norm of the tracking error of a constrained limiting optimal compensator.