H∞ based stabilization and disturbance attenuation for nonlinear differential repetitive processes with an iterative learning control application

Repetitive processes propagate information in two independent directions and arise in the modeling of industrial systems such as metal rolling. Also iterative learning control law design can be undertaken in a repetitive process setting and for linear dynamics such designs have been experimentally verified. This paper addresses stabilization and disturbance attenuation for differential nonlinear repetitive processes where vector Lyapunov functions are used to characterize a physically relevant stability property and the disturbance attenuation is expressed in terms of an H∞ norm. An extension to processes with failures modeled by a finite state Markov chain is also developed and applied to iterative learning control design in the presence of model uncertainty and sensor failures.