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

This paper develops a new set of necessary and sufficient conditionsfor the stability of linear repetitiveprocesses, based on a dissipative setting for analysis. Theseconditions reduce the problem of determining whether a linearrepetitive process is stable or not to that of checking for theexistence of a solution to a set of linear matrixinequalities (LMIs). Testing the resulting conditions only requirescomputations with matrices whose entries are constant in comparison toalternatives where frequency response computations are required