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Double Inverted pendulums are typical examples of unstable systems and have been used for the verification of designed control systems and control education in laboratories. This paper proposed a robust multi-objective state feedback controller for a double inverted pendulum system using the satisfaction additional constraints. Mixture of different synthesis specifications such as the guarantees H∞ performance, minimizes H2 performance and regional pole placement constraints, which are converted into the Linear Matrix Inequality (LMI). Then convex program minimized linear objective under LMI constraints is applied. The robust state feedback controller is designed and simulated in MATLAB and results show that the system with the proposed state feedback controller has a good response to initial condition with respect to parameters of output performance. The simulation is also displayed a system with proposed controller is robust against input disturbances and plant uncertainty. [ABSTRACT FROM AUTHOR]