  Online convex optimization (OCO) is a powerful tool for learning sequential
data, making it ideal for high precision control applications where the
disturbances are arbitrary and unknown in advance. However, the ability of
OCO-based controllers to accurately learn the disturbance while maintaining
closed-loop stability relies on having an accurate model of the plant. This
paper studies the performance of OCO-based controllers for linear
time-invariant (LTI) systems subject to disturbance and model uncertainty. The
model uncertainty can cause the closed-loop to become unstable. We provide a
sufficient condition for robust stability based on the small gain theorem. This
condition is easily incorporated as an on-line constraint in the OCO
controller. Finally, we verify via numerical simulations that imposing the
robust stability condition on the OCO controller ensures closed-loop stability.
