This paper deals with structured feedback gain design problems for linear time invariant systems. Linear matrix inequality (LMI) conditions with structured LMI variables are derived via stabilizable dilation which is proposed in this paper. Stabilizable dilation is to extend both the state space of the system and the space of the structured feedback gain without loss of stabilizability of the system. Since the number of LMI variables becomes large after its dilation, the LMI problem via stabilizable dilation could be feasible even if the LMI problem without its dilation is infeasible. It is demonstrated through a numerical example. Furthermore, it is shown that, if the problem without dilation is feasible, the problem with dilation is always feasible.