On the Controllability and Observability of Heterogeneous Networked Systems with distinct node dimensions and inner-coupling matrices

In this study we consider the controllability and observability of networked systems with higher-dimensional nodes following heterogeneous dynamics, assembled in a weighted and directed topology. In addition to the heterogeneity in node dynamics, the dimensions of the nodes as well as the inner-coupling matrices can be different. Previously defined networked system models with higher-dimensional MIMO-LTI nodes can be viewed as particular cases of the model considered in this paper. Owing to this generality, existing results on the controllability of homogeneous networked systems that establish the dependency of system controllability on factors like network topology, individual node dynamics and inner interactions are extended to the system under consideration. We have extended a necessary and sufficient condition and three necessary conditions for network controllability. Furthermore, a necessary and sufficient condition for the observability of the networked system is derived. Special cases where node systems are assembled in path, star and wheel topologies are also analysed.