Well-posedness & stability analysis for spatially interconnected systems with finite extent

Novel sufficient conditions for well-posedness and stability of spatially interconnected systems with finite extent are proposed. Existing conditions for space-invariant interconnected systems do in general not guarantee these properties for finite-extent systems. Rather than using a model based on the spatial shift operator, here the system is represented as a network of (not necessarily identical) subsystems with a particular interconnection topology. The analysis problem is solved by utilizing the full-block S-procedure; by imposing a suitable structure on the associated multiplier the problem can be reduced to a complexity that does not depend on the size of the network but only on the size of a single subsystem and the number of different subsystem types present in the network. Various boundary conditions can be taken into account. The proposed method is illustrated on the model of a thermal rod equipped with an array of sensors and actuators.