The problem of designing static output-feedback epsilon-independent controllers for linear time-invariant singularly perturbed systems is considered. The controller is required to satisfy a prescribed H-infinity-norm bound and to minimize the closed-loop entropy (at s = infinity) for all small enough epsilon. The optimal controller gain is designed on the basis of generalized Riccati and Lyapunov equations with symmetric block (2,2), that are coupled via a projection. This gain is either purely fast, purely slow or a composite one, depending on the structure of the output coupling matrix. A well-posed problem with a finite value of entropy for epsilon --> 0 is obtained by assuming that the entropy of the fast subproblem is zero or by scaling the matrices of the system. In the first case the optimal controller is the one that minimizes the entropy of the corresponding descriptor system.