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This paper studies the sliding mode control (SMC) law design problem of a class of positive systems with Lipschitz nonlinearities. We aim to devise a proper SMC law to drive the sliding mode dynamics onto the designated sliding mode surface. By choosing proper Lyapunov functions, the positiveness and the asymptotic stability of the closed-loop SMC system are guaranteed by the presented sufficient conditions. The SMC law design problem can be solved by a linear matrix inequalities technique. In the end, the feasibility and the validity of the raised method are provided by the simulation results.