In this paper, stabilization and trajectory tracking control of the double inverted pendulum (DIP) as a benchmark under actuated highly nonlinear dynamical system, attributed with specific control complexities using hybrid observer based indirect fuzzy adaptive control is investigated. Due to inherent nature of the process that the equal number of control inputs as the degrees of freedom of the plant are not available, therefore, setting up the control action faces with serious challenges. Meanwhile, inaccessibility assumption to some state parameters as the most important factor in designing the controller by means of the proposed control method is for the first time addressed stabilizing the specified plant in this research. In order to illustrate the performance of the proposed approach, specific simulation software is developed in Matlab/Simulink platform. Set of conducted simulation results and comparative studies with the published papers addressing the same aim, showing the capability and excellence of the proposed hybrid fuzzy adaptive observer control approach achieving the targets in terms of establishing stabilization, trajectory tracking and robustifying the under controlled plant.