Stabilization of differential repetitive processes

Differential repetitive processes are a subclass of 2D systems that arise in modeling physical processes with identical repetitions of the same task and in the analysis of other control problems such as the design of iterative learning control laws. These models have proved to be efficient within the framework of linear dynamics, where control laws designed in this setting have been verified experimentally, but there are few results for nonlinear dynamics. This paper develops new results on the stability, stabilization and disturbance attenuation, using an $H_\infty$ norm measure, for nonlinear differential repetitive processes. These results are then applied to design iterative learning control algorithms under model uncertainty and sensor failures described by a homogeneous Markov chain with a finite set of states. The resulting design algorithms can be computed using linear matrix inequalities.