Controllability and observability of networked singular systems

The controllability and observability of networked systems are studied, where the network topology is directed and the nodes are time‐invariant singular linear systems. Under the regularity assumption, a specific condition for the R‐controllability of the network with single‐input single‐output node‐systems is first established. Furthermore, necessary and sufficient conditions are derived for the R‐controllability and C‐controllability of the network with multi‐input multi‐output node systems. It is shown that the controllability of the overall system is an integrated result of the network topology, the subsystem dynamics, the external inputs, and the inner interactions. Additionally, corresponding observability criteria for such systems are also obtained, which indicate that the observability of the whole system depends only on the parameters of its subsystem. Finally, several examples are given to illustrate the proposed results.