Control Law Design for Switched Repetitive Processes with a Metal Rolling Example

Discrete linear repetitive processes are a distinct class of 2D systems where the information propagates in two independent directions, one of which is limited to a finite and fixed duration or interval. Recently, applications areas have been uncovered where suitably developed system theory for repetitive processes whose dynamics switch in one or other of the two independent directions of information propagation has potentially much to contribute. In this paper, we continue previous work in this general area by developing an efficient and numerically reliable solution to the stabilization problem, i.e. the design of a control law to ensure stability for the case of more complicated switching schemes and, in particular, when more than two different models are the subject of switching. The results are in the form of sufficient conditions which can be implemented through the use of the linear matrix inequality (LMI) algorithms.