Stability tests for a class of differential linear repetitive processes with dynamic boundary conditions

Repetitive processes are a distinct class of 2D systems of both practical and theoretical interest. Their essential characteristic is repeated sweeps, termed passes, through a set of dynamics defined over a finite duration with explicit interaction between the outputs, or pass profiles, produced as the process dynamics evolve. Experience has shown that these processes cannot be studied/controlled by direct application of existing theory. This fact, and the growing list of applications areas, has prompted an ongoing research programme into the development of a `mature´ systems theory for these processes for onward translation into reliable generally applicable controller design algorithms. This paper develops stability tests for a sub-class of so-called differential linear repetitive processes in the presence of a general set of initial conditions, where it is known that the structure of these conditions is critical to their stability properties