This paper presents a methodology in the Linear Matrix Inequality (LMI) framework to jointly optimize the linear control law and the linear parameters in the plant. The paper solves an integrated plant and control design problem which bounds the covariance of selected outputs. The method simultaneously designs the plant parameters and the controller. The proposed method also allows one to guarantee bounds on the peak response in the presence of bounded energy excitations. With minor modifications, the method can also guarantee bounds on the H_∞ performance and many other convex performance criteria. The nonconvex problem is approximated by a convex one by adding a certain function to make the constraint convex. This convexifying function is updated with each iteration until the added convexifying function disappears at a saddle point of the nonconvex problem.