In the design of an observer-based LMI(linear matrix inequality)controller, bivariate values appear in one linear matrix inequality. To solve this problem, we propose an initial value-iteration method in this paper. Of the bivariate values, one is a positive definite matrix variable and the other is a scalar. Considering these two characteristics, we take the positive definite matrix variable as the initial value, in order to ensure the astringency of the iteration and to meet the requirements of positive definite matrices. Simulation analysis shows that the designed controller can guarantee the control trend, which was far from the expected control result. We subsequently put forward the concept of a regulatory factor. As a case study, the simulation analysis of a three-storey benchmark building shows that the proposed method is feasible.