H∞ control of linear time-invariant singularly perturbed systems is considered. A sequential procedure is described to decompose the problem into slow and fast subproblems. The fast problem is solved first. Then the slow problem is solved under a constraint on the value of the compensator at infinity. A composite compensator is formed as the parallel connection of the fast compensator with the strictly proper part of the slow compensator. The asymptotic validity of the composite compensator is established.