Dissipative stability theory for linear repetitive processes with application in iterative learning control

This paper develops a new set of necessary and sufficient conditions for the stability of linear repetitive processes, based on a dissipative setting for analysis. These conditions reduce the problem of determining whether a linear repetitive process is stable or not to that of checking for the existence of a solution to a set of linear matrix inequalities (LMIs). Testing the resulting conditions only requires compu- tations with matrices whose entries are constant in comparison to alternatives where frequency response computations are required

Repetitive Process based Iterative Learning Control designed by LMIs and Experimentally Verified on a Gantry Robot

In this paper we use a 2D systems setting todevelop new results on iterative learning control for linearsingle-input single-output (SISO) plants, where it is well knownin the subject area that a trade-off exists between speed ofconvergence and the response along the trials. Here we givenew results by designing the control scheme using a strong formof stability for repetitive processes/2D linear systems known asstability along the pass (or trial). The design computations arein terms of Linear Matrix Inequalities (LMIs) and results fromexperimental verification on a gantry robot are also given