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In this paper, we derive a new analytical state-space model for semiconductor optical amplifier (SOA) dynamics with nonlinear gain compression. We show that a multichannel closed-form state-space model is possible with polynomial gain compression and position-independent carrier density. The compressed model is significantly more accurate than existing noncompressed models as demonstrated by comparison with pump-probe experiments: response magnitude and recovery time are more accurately modeled with explicit gain compression. We then apply the model to design an optical feedback controller that regulates the total optical power at the output of a gain-compressed SOA.