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This paper studies near-controllability of a class of discrete-time bilinearsystems via a root locus approach. A necessary and sufficient criterion for thesystems to be nearly controllable is given. In particular, by using the rootlocus approach, the control inputs which achieve the state transition for thenearly controllable systems can be computed. Furthermore, for the non-nearlycontrollable systems, nearly-controllable subspaces are derived andnear-controllability index is defined. Accordingly, the controllabilityproperties of such class of discrete-time bilinear systems are fullycharacterized. Finally, examples are provided to demonstrate the results of thepaper.

On Near-controllability, Nearly-controllable Subspaces, and  Near-controllability Index of a Class of Discrete-time Bilinear Systems: A  Root Locus Approach