Semiconductor optical amplifiers (SOAs) are attractive for integrated photonic signal processing, but because their response is so fast, delays in a controller feedback path can jeopardize performance and stability. Using state-space methods, we quantify the constraints imposed on feedback controllers by closed-loop delay. We first derive a complete nonlinear state-space control model of a SOA with an equivalent circuit containing parasitics and dynamic impedance; the analytical state-space model agrees well with a validated photonic-only control model. Using a linearized version of the model we demonstrate that time delay in the feedback path can destabilize the SOA through phase accumulation. We then apply linear system theory to calculate the best-case stable delay margin for a given controller norm, and find a potentially severe inverse relationship between delay margin and controller norm. Finally, guided by the delay-controller relationship we design a hybrid feedforward-feedback controller to illustrate that good transient and steady-state regulation is obtained by carefully balancing the feedforward and feedback components. Our state-space modeling and design methods are general and are easily adapted to the design and analysis of more complex photonic circuits.