To address the issue of inadequate control effect resulting from the challenge of measuring state feedback information comprehensively, this paper proposes an iterative output feedback energy-to-peak control method that solely depends on partial external observation data. This paper presents the computational steps for achieving a suboptimal solution to the output feedback bilinear matrix inequality constrained problem using an iterative linear matrix inequality approach. The proposed method overcomes the challenge of numerically solving the optimization problem. The unknown variables in the output feedback linear matrix inequality optimization problem are transformed equivalently to obtain a new linear matrix inequality optimization problem. The numerical results of the two optimization problems are then used to iterate with each other and obtain a suboptimal solution. A comprehensive analysis was conducted on an 8-story building structure, utilizing state feedback, output feedback, and iterative output feedback energy-to-peak control techniques. The results of the study indicate that the proposed iterative output feedback energy-to-peak control approach efficiently reduces the displacement and acceleration response of the structure, exhibiting superior control effectiveness than both the state feedback and output feedback energy-to-peak control methods. The findings demonstrate the practicality and versatility of the suggested method.