Robust iterative learning control design is straightforward for uncertain LTI systems satisfying the robust performance condition

This note demonstrates that the design of a robust iterative learning control is straightforward for uncertain linear time-invariant systems satisfying the robust performance condition. It is shown that once a controller is designed to satisfy the well-known robust performance condition, a convergent updating rule involving the performance weighting function can be directly obtained. It is also shown that for a particular choice of this weighting function, one can achieve a perfect tracking. In the case where this choice is not allowable, a sufficient condition ensuring that, the least upper bound of the L-2-norm of the final tracking error is less than the least upper bound of the L-2-norm of the initial tracking error is provided. This sufficient condition also guarantees that the infinity-norm of the final tracking error is less than the infinity-norm of the initial tracking error.