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. Such models occur in transportation systems, in chemical processes, in production systems, in communication systems, and in models of boilers in nuclear power plants. 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 stuided in the literature. Next we obtain necessary and sufficient conditions for input-output stability. An example illustrates the application of the test.