An algebraic approach to iterative learning control

In this paper discrete-time iterative learning control (ILC) systems are analysed from an algebraic point of view. The algebraic analysis shows that an ILC synthesis problem can be considered as a tracking problem of a multi-channel step-function. Furthermore, the plant to be controlled is a static multivariable plant. Another major contribution of this paper is a general convergence theory of ILC systems in terms of their closed-loop poles. This convergence theory shows that time-variant ILC control laws should be typically used instead of time-invariant control laws in order to guarantee good transient tracking behaviour. Simulations high-light the different theoretical findings in this paper.