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In this paper, we present a feedback control law for a class of bilinear plant. It exhibits a bang-bang structure using a linear switching function. Asymptotic stability of the closed-loop system is derived by applying a generalized version of the Lyapunov's direct method. The primary advantage of our approach lies in its simplicity, indicating that the field of potential applications is quite wide. In order to test use and effectiveness of the procedure, the practical case of a continuous stirred tank reactor is investigated by digital simulation.