In many studies cases, generating a control laws using the state and/or output variables in Reciprocal State Space (RSS) form can be more easy than in Standard State Space (SSS) one. The formulation of a new stabilization control problem using feedback principle for linear discrete-time systems in RSS is presented in this brief. In contrast to the existing approaches, the considered model is described in RSS framework with an extension to Lipschitz nonlinear discrete-time systems. The asymptotic stability based on Lyapunov functions of the closed-loop system is guaranteed. The control design resolution problem is ensured through the Linear Matrix Inequalities (LMI) technique, the lemmas and the use of slack-variables and Differential Mean Value Theorem (DMVT). The performance of the proposed approach are shown through the experimental results using Real Time Implementation (RTI) with an Arduino MEGA 2560 board.