Robust stability for iterative learning control

The phenomenon of long term instability of iterative learning control systems is examined. The concept of stability with respect to a specified trajectory is used to define a nonlinear biased gap metric. The resulting robust stability theorem, applied in a 2D setting, is used to prove the robust stability of a set of ILC algorithms engaged in trajectory tracking. The robust stability guarantee is dependent on the gain of the system from input and output disturbances to internal signals. This gain is calculated for a set of linear ILC algorithms to provide a guide to the trade-offs between tracking accuracy and robust stability.