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This paper completely solves the controllability problems of two-dimensionalmulti-input discrete-time bilinear systems with and without drift. Necessaryand sufficient conditions for controllability, which cover the existingresults, are obtained by using an algebraic method. Furthermore, for theuncontrollable systems, near-controllability is studied and necessary andsufficient conditions for the systems to be nearly controllable are alsopresented. Examples are provided to demonstrate the conceptions and results ofthe paper.

On Controllability and Near-controllability of Multi-input Discrete-time Bilinear Systems in Dimension Two