Mixed H₂/H_∞ control approach and its application in satellite attitude control system

In this paper, we address the mixed H₂/H_∞ control approach for linear time-invariant system based on linear matrix inequality (LMI). First, the problem to be solved is stated, and the satellite attitude dynamics is established and converted into a corresponding state space form. Then, the mixed H₂/H_∞ controller based on LMIs is designed in order to attain the state feedback gain matrix. To validate the efficiency and practicability of the proposed controller, simulation results based on satellite attitude system are presented, from which we can observe that under the condition of external disturbances, the system will be stable within 150s, and the maximum of control torque will be no more than 0.025Nm. Expanding the controller gain will affect the stabilizing process, but not the stabilization time, and it will increase the control input which will bring pressure to the actuator.