In this paper, we deal with the problem to find a static feedback gain matrix which satisfies multiple control specifications described in LMIs. This problem is easily solved when the intersection of all the sets of solutions of LMIs is not empty. However, even if it is empty, the gain matrix which satisfies all the specifications can exist. In this case, the problem to find such a matrix is equivalent to finding a linear subspace which intersects all the sets. We propose an algorithm to solve this problem. Some theoretical aspects are considered in a special case. Numerical experiments show the effectiveness of the algorithm.