Discrete-time iterative learning control for relative degree systems: A 2-D approach

This paper is devoted to the two-dimensional (2-D) design problem that arises from discrete-time iterative learning control (ILC). For linear time-invariant (LTI) systems with well-defined relative degree, a unified ILC algorithm is considered which provides wider freedom for the updating law formation. It demonstrates that an appropriately defined variable, together with the tracking error, can be employed to establish the Roesser systems based 2-D description of the ILC process. This enables both asymptotic stability and monotonic convergence of the relative degree ILC systems to be achieved. In particular, conditions for the monotonic convergence are described in terms of linear matrix inequalities (LMIs), which directly give formulas for the updating law design.