Mixed H₂/H_∞ state feedback attitude control of microsatellite based on extended LMI method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system, to avoid the adverse effects, this paper investigates the mixed H₂/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method. Firstly, the microsatellite attitude control system is established and transformed into corresponding state space form. Then, without the equivalence restriction of the two Lyapunov variables of H₂ and H_∞ performance, this paper introduces additional variables to design the mixed H₂/H_∞ control method based on LMI which can also reduce the conservatives. Finally, numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not. The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.