In this paper, a method is proposed for integrated design of mechatronics systems. The integrated design problem is formulated as a semi-definite programming optimization problem. However, this is an infinite dimensional convex optimization problem, which is hard to solve. In this paper, it is shown that a vertex enumeration method can be used to transform the infinite dimensional optimization problem into a finite dimensional problem, which under the assumptions that the state space matrices are affine function of structural variables and that the structural variables belong to a polytope, can be solved efficiently. To show the effectiveness of the method, the method is applied to a mechatronics system.