This paper addresses the control design problem for linear singularly perturbed systems subject to bounded control. The singular perturbation method is used to define reduced and well-behaved control problems. Constructive geometric conditions are proposed to derive a stabilizing controller in both a composite or reduced contexts and a set of admissible initial state from which the closed-loop stability is ensured. Convex optimization problems with LMI constraints are proposed in order to select the feedback gain allowing to enlarge the region of stability. An illustrative example shows the effectiveness of the proposed techniques.