Dissipative Stabilization of Nonlinear Repetitive Processes with an Iterative Learning Control Application

Repetitive processes arise in the modeling of physical systems and have a 2D systems structure as there are two directions of information propagation, one of which is spatial and the other is time over a finite duration. Recently, a stability theory for nonlinear repetitive processes has been developed. This paper uses nonlinear stability theory to develop a parameterized control law for linear dynamics. Applied to iterative learning control law design, this law allows for gain scheduling tuning to achieve better performance. The new design is illustrated by application to an example where the model representing the dynamics has been obtained by frequency response test data obtained from a physical example.