Interconnected linear multivariable systems with delays: System properties and input-output stability

We consider an arbitrary interconnection of linear, time-invariant, distributed, multivariable subsystems; each subsystem is represented either by a strictly proper rational transfer function or by a finite sum of pure delay terms. Allowing inputs to be applied to any interconnection point, we show that, except for a special case, the input-output transfer function of such a system is in a class extensively studied in the literature. Next we obtain necessary and sufficient conditions for input-output stability. An example illustrates the application of the test.