Stability analysis and stabilization of discretized uncertain spatially interconnected systems

In this paper spatially interconnected (ladder) systems have been discussed. First, the multidimensional, in that case, 2D - continuous in time and discrete in the spatial variable, has been introduced. Next, the temporal dynamics has been discretized, which has allowed to create the general, discrete model for the system dynamics. It has been assumed that system elements are the subject of uncertainty of the norm bounded form. Finally, robust stability testing and robust stabilizing controller design conditions have been proposed and its effectiveness is illustrated by an simulation example.