Balanced truncation of linear systems interconnected over arbitrary graphs with communication latency

This paper deals with the model reduction of spatially distributed systems. In particular, we treat discrete-time linear time-varying subsystems interconnected over arbitrary graph structures and subjected to communication latency, a one step time delay on the information exchange between the source and the target subsystems. We propose a generalization of the balanced truncation scheme, apply it to the model reduction of distributed systems, and derive a guaranteed upper bound on the resultant error. This bound reduces to a finite sum in the case of periodic and time-invariant subsystems.