Detection of Delays and Feedthroughs in Dynamic Networked Systems

This letter presents systematic tests to determine if a particular transfer function in an interconnected system is strictly proper or has a feedthrough. Considering a strictly proper module between two nodes in a networked system, if only the data of the two nodes are used, there are situations where numerical tests to determine if the module is strictly proper will fail. It is shown, however, that marginalizing some of the nodes of a networked system under certain conditions preserves delays and feedthroughs in certain links. Therefore, using a set of auxiliary nodes that satisfies certain conditions, it is possible to design a systematic test to determine if a module in the networked system is strictly proper. The conditions are proven to be sufficient. Similar ideas are used to formulate a systematic test to determine if a module has a feedthrough.