  This work introduces a controller synthesis method via system level synthesis
for nonlinear systems characterized by polynomial dynamics. The resulting
framework yields finite impulse response, time-invariant, closed-loop transfer
functions with guaranteed disturbance cancellation. Our method generalizes
feedback linearization to enable partial feedback linearization, where the
cancellation of the nonlinearity is spread across a finite-time horizon. This
provides flexibility to use the system dynamics to attenuate disturbances
before cancellation via control, reducing the cost of control compared with
feedback linearization while maintaining guarantees about disturbance
rejection. This approach is illustrated on a benchmark example and on a common
model for fluid flow control.
