The problem of designing static output-feedback controllers is considered, The controller is required to minimize the closed-loop entropy (at s = infinity) and to satisfy a prescribed H-infinity-norm bound. The design equations consist of a modified Riccati equation and a Lyapunov equation that are coupled via a projection. These equations are solved using a homotopy algorithm. The design procedure is illustrated by two examples, The first is a classical example that was solved in the literature using convex optimization techniques. The second example is one of designing a gain-scheduled normal acceleration loop for an airlaunched unmanned air vehicle.