Space Sampling Effects in Nonlinear Distributed System Stability

The purpose of this paper is to determine, from a practical point of view, the effects of a space sampling on the input-output stability, and the absolute stability of distributed parameter systems with distributed control. Three models are proposed which involve, respectively, transfer functions in space and time, Laplace-Green’s functions, and distributed transfer functions. It is shown that the first model is the most pessimistic, but in contrast is the easiest to use. While the first model applies to system with constant coefficients only, the other ones can be used with constant or space dependent coefficients.