Iterative learning control for discrete linear systems with Zero Markov parameters using repetitive process stability theory

This paper considers iterative learning control for the practically relevant case of deterministic discrete linear plants where the first Markov parameter is zero. A 2D systems approach that uses a strong form of stability for linear repetitive processes is used to develop a one step control law design for both trial-to-trial error convergence and along the trial performance. The resulting design computations are completed using linear matrix inequalities, and results from applying the control law to one axis of a gantry robot are also given by way of experimental verification.