Controllability Analysis of Singular Heterogeneous Networked Systems

This paper investigates the controllability issue of networked dynamic systems with heterogeneous singular sub-systems. First, it analyzes the necessary conditions affecting system controllability. The results indicate that the observability of singular subsystems and the controllability of the system <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(E_{i},\ A_{i},\ H_{i})$</tex> are necessary conditions for the controllability of networked systems; however, a networked system may still be controllable even if the network topology or subsystems are uncontrollable. Then, the paper provides the necessary and sufficient conditions for controllability under general network topologies. It reveals the impact of factors such as network topology structure, external inputs, subsystem dynamics, and state couplings between subsystems on the controllability of singular heterogeneous networked systems. Additionally, it examines the necessary and sufficient conditions for controllability when the network topology matrix is diagonalizable. Finally, several examples are provided to illustrate the results of the study.