We deal with an integrated design problem of structural and control systems. For a plant with unstable poles and zeros we consider a design problem of the plant itself for minimizing the closed-loop H-infinity norm. The design parameter of the optimal design problem is the location of unstable poles and zeros of the plant. The achievable minimum., norm of the closed-loop system can be obtained just by examining the determinant of Pick matrix defined by the unstable poles and zeros of the plant. We show the analytic relation between the unstable poles/zeros and the optimal closed-loop H-infinity norm for a class of plants with two unstable poles (and/or zeros). In the general case (the number of unstable poles/zeros is more than three) the optimal design problem can be formulated as a minimization of the maximum eigenvalue in a generalized eigenvalue problem related to Pick matrix.