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This paper presents graph theoretic conditions for the controllability andaccessibility of bilinear systems over the special orthogonal group, thespecial linear group and the general linear group, respectively, in thepresence of drift terms. Such bilinear systems naturally induce two interactiongraphs: one graph from the drift, and another from the controlled dynamics. Asa result, the system controllability or accessibility becomes a property of thetwo graphs in view of the classical Lie algebra rank condition. We establish asystemic way of transforming the Lie bracket operations in the underlying Liealgebra, into specific operations of removing or creating links over the driftand controlled interaction graphs. As a result, we establish a series ofgraphical conditions for the controllability and accessibility of such bilinearsystems, which rely only on the connectivity of the union of the drift andcontrolled interaction graphs. We present examples to illustrate the validityof the established results, and show that the proposed conditions are in factconsiderably tight.

Controllability and Accessibility on Graphs for Bilinear Systems over Lie Groups