Boundary conditions and the stability of a class of 2D continuous-discrete linear systems

Differential linear repetitive processes are characterized by a series of sweeps, or passes, through a set of dynamics defined over a finite interval or duration with interaction between successive passes. They are distinct from other classes of 2D continuous-discrete linear systems due to the fact that information propagation in one of the two separate directions only occurs over a finite duration. Moreover, this is an intrinsic feature of the underlying dynamics as opposed to an assumption introduced for analysis purposes. This paper shows that the structure of the initial conditions at the start of each new pass of the process is critical to its stability properties.