In this paper, a new iterative algorithm is developed using control theoretic approach to find the minimum norm solution of underdetermined problems. The minimum norm solution is obtained by applying the $H∞$ optimization technique. The accuracy and convergence rate of the proposed algorithm are ensured using the framework of linear feedback control theory. The performances of the proposed method, the QR decomposition method, and the least square minimal residue (LSMR) method are compared numerically. The number of iterations in the proposed algorithm is comparable with the LSMR method. Finally, the developed algorithm is applied to the control allocation problem and its effectiveness is demonstrated through a detailed simulation study.

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