Repetitive Learning Control Design and Period Uncertainties

Abstract

Abstract 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.