Temporal discretization of spatially distributed systems

There have been efforts previously to use multidimensional system representations for the control of spatially distributed systems. By expressing spatially distributed systems as multidimensional system models, it has been shown that semidefinite programming techniques can be used for control design and analysis. This formulation can in fact be interpreted as the natural generalization of linear fractional transformation based robust control tools to spatially distributed systems. While most models of physical systems are continuous time models, discrete models are required for control implementation. In this paper, we address the issue of constructing discrete time models from continuous time models for spatially distributed systems.