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In this paper it is presented the design of a controller for a reaction wheel pendulum using a discrete-time representation via optimal control from the point of view of passivity-based control analysis. The main advantage of the proposed approach is that it allows to guarantee asymptotic stability convergence using a quadratic candidate Lyapunov function. Numerical simulations show that the proposed inverse optimal control design permits to reach superior numerical performance reported by continuous approaches such as Lyapunov control functions and interconnection, and damping assignment passivity-based controllers. An additional advantage of the proposed inverse optimal control method is its easy implementation since it does not employ additional states. It is only required a basic discretization of the time-domain dynamical model based on the backward representation. All the simulations are carried out in MATLAB/OCTAVE software using a codification on the script environment.