Strong Structural Controllability and Observability of Individual Nodes: A Graph-Theoretical Approach

In this article, we first establish definitions of structural controllability and strong structural observability for a single state node, based on the conditions of strong structural controllability and observability outlined in existing works. Second, we provide a necessary and sufficient condition for strongly structurally controllable (SSC) and strongly structurally observable (SSO) state nodes in acyclic graphs. Third, we provide the relationship between the conditions for SSC and SSO state nodes with the fixed controllable and observable nodes used in the existing literature. As a practical application of SSC and SSO state nodes, we introduce structural Kalman decomposition, an innovative technique that utilizes the information from these state nodes for robust system dynamics analysis under parameter uncertainties.