Classification of the Structurally Controllable Zero-Patterns for Driftless Bilinear Control Systems

We introduce and study the structural controllability of driftless bilinear control systems. We study two cases: in the first, the system matrices belong to one zero-pattern, and in the second, the system matrices belong to one of several zero-patterns. We refer to them as single and multiple patterns cases. In both cases, we prove that the structural controllability of driftless bilinear control systems is a generic property. We also classify the structurally controllable zero-patterns based on the strong connectivity of their corresponding graph. We provide algorithms that compute the minimum number of matrices needed for the structural controllability of driftless bilinear systems. The results about the structural controllability of driftless bilinear systems can be also used for the study of the structural accessibility of bilinear systems with drift term.