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This paper gives necessary and sufficient conditions for the invertibility of a class of nonlinear systems which includes matrix bilinear systems. Lie algebraic invertibility criteria are obtained for bilinear systems in Rⁿ which generalize the standard tests for single input linear systems. These results are used to construct nonlinear systems which act as left-inverses for bilinear systems.
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Ronald M. Hirschorn (1977) studied this question.
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