This paper proposes a design of new Sliding Mode Control (SMC) for Lipschitz nonlinear systems in a new Reciprocal State Space (RSS) framework. The main objective is to extend the state derivative feedback stabilization methods in SMC designs. The presented SMC law involves the use of RSS feedback approach based on the proper Lyapunov functions. The asymptotic stability of the closed-loop SMC system is guaranteed by two forms of Sliding Mode Surface (SMS). The first method deals with the use of Standard Sliding Function (SSF). The second one is developed with an Integral-type Sliding Function (ISF). The SMC law design resolution problem is ensured through a Linear Matrix Inequalities (LMI) technique under certain conditions. Experimental results show high performances of the proposed approach using Real Time Implementation (RTI) with Digital Signal Processing (DSP) device (DSpace DS 1104).