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In this paper, we study graphical conditions for structural controllabilityand accessibility of drifted bilinear systems over Lie groups. We consider abilinear control system with drift and controlled terms that evolves over thespecial orthogonal group, the general linear group, and the special unitarygroup. Zero patterns are prescribed for the drift and controlled dynamics withrespect to a set of base elements in the corresponding Lie algebra. The driftdynamics must respect a rigid zero-pattern in the sense that the drift takesvalues as a linear combination of base elements with strictly non-zerocoefficients; the controlled dynamics are allowed to follow a free zero patternwith potentially zero coefficients in the configuration of the controlled termby linear combination of the controlled base elements. First of all, for suchbilinear systems over the special orthogonal group or the special unitarygroup, the zero patterns are shown to be associated with two undirected ordirected graphs whose connectivity and connected components ensure structuralcontrollability/accessibility. Next, for bilinear systems over the specialunitary group, we introduce two edge-colored graphs associated with the driftand controlled zero patterns, and prove structural controllability conditionsrelated to connectivity and the number of edges of a particular color.

Structural Controllability on Graphs for Drifted Bilinear Systems over Lie Groups