Stability of slowly varying spatiotemporal systems

A characterization of stability for slowly varying spatiotemporal systems based on input-output description of the plant and controller is presented. This approach generalizes the results developed for the standard case for slowly time-varying systems. The controller design is based on frozen spatially and temporally invariant descriptions of the plant. In particular, we consider the case where the controllers are not necessarily adjusted for every instance in space and time, and hence are used for some fixed window in time and space before new controllers are implemented. It is shown that the actual spatiotemporally varying system can be stabilized using frozen in space and time controllers, provided the variations in the spatiotemporal dynamics are sufficiently small.