The inertia wheel inverted pendulum belongs to the class of underactuated mechanical systems [12] [10] [22]. These systems are characterized by less control inputs than degrees of freedom, meaning that they have at least one unactuated generalized coordinate. Underactuation in these systems has two main sources, the first one is intentionally, i.e. decided in the design stage to minimize the cost, the weight, consumption, etc. The second is non-intentionally, where a fully actuated mechanical system can become underactuated after the deficiency of one or more actuators. Underactuated mechanical systems are characterized by a high nonlinear coupling between actuated and unactuated coordinates [7], and an internal dynamics which is often unstable (i.e. non minimum phase Systems [2]). In the real world many examples of such systems exist, they include, among others, Inverted pendulums [21] [18], under-actuated robot manipulators [6], gymnast robots [31] [23], undersea vehicles [17], aircrafts [26], and some mobile robots [20]. The inertia wheel inverted pendulum [34] is a benchmark for nonlinear control of underactuated mechanical systems. I has attracted the attention of many researchers within control community. Indeed, different control solution have been proposed in the literature these last decades. In [1], strong damping force on the inertia wheel is taken into account in the design of the controller. The stabilization is achieved via nested saturation based controller. [19] solves the limit cycles generation problem on the inertia wheel pendulum using virtual holonomic constraints. Real-time experiments were carried out showing the robustness of the proposed approach. In [27], collocated partial feedback linearization was performed to exhibit the nonlinear core subsystem which is stabilized using an implicit control. The remaining subsystem is stabilized using multiple sliding mode control technique. In our previous work [4] [5], non-collocated partial feedback linearization is used; this gives rise to an unstable internal dynamics, which is stabilized using trajectory optimization and model-based error estimation. In [36] a generalized predictive controller is proposed for the stabilization of the inertia wheel inverted pendulum. In [9], the proposed control solution deals with external disturbance rejection in passivity based control 1