We consider an integrated design problem of structural and control systems. It is well known that even the simplest formulation of this problem results in a kind of a BMI problem. In this paper, homotopy-like iterative design method based on LMIs is proposed to obtain an optimal plant and a controller simultaneously for a full-order output feedback problem. We can deal with a multiobjective problem, e. g., H-2/H-infinity control problem etc. in the proposed design method. We can also optimize structural design parameters appearing non-linearly in the coefficient matrices of the plant state space form using the first order approximation of the non-linear dependence in the proposed algorithm. Several design examples show that the proposed algorithm works quite effectively for various integrated design problems.