Repetitive learning control design and period uncertainties

The aim of this brief is to show how stability proofs in the time-domain involving suitable quadratic-integral Lyapunov-like functions can be derived in the repetitive control design scenario in the case of uncertain period for the reference signals/disturbances to be tracked/rejected. Even though the presented arguments are rather general, we apply them to the generalization of the proportional-integral-derivative (PID)-like learning control that has been recently designed. The use of the presented results in multi-link robot synchronization tasks provides simple and intuitive solutions to as yet unsolved problems.