On the well-posedness of large-scale interconnected systems

In this paper, we give a precise definition of well-posedness for a large-scale interconnected system, and derive several criteria for well-posedness. In the case of nonlinear systems, the criteria presented here are sufficient conditions for well-posedness, but they are graph-theoretic in nature and have a nice physical interpretation, both for continuous-time as well as discrete-time systems. In the case of linear time-invariant continuous-time systems, necessary and sufficient conditions for well-posedness are presented. Linear time-invariant discrete-time systems are not discussed here as they are adequately discussed elsewhere.