Strong Structural Controllability of Linear Descriptor Systems

This paper explores the controllability of linear descriptor systems on graphs. These systems, which are a generalization of linear time-invariant systems, are widely used for modeling various real-life phenomena with equations that include both algebraic and differential terms. There are three main types of controllability for these systems: controllability within a reachable set (R-controllability), complete controllability (C-controllability), and impulse controllability (I-controllability). This work focuses on strong structural controllability, which refers to the ability to control a family of linear descriptor systems with the same underlying directed graph structure. To this end, different graphs are defined, and a correspondence between zero forcing sets of these graphs and the sets of control nodes required for strong structural R-controllability, C-controllability, and I-controllability is established.