We consider the singularly perturbed H-infinity control problem under perfect state measurements, for both finite and infinite horizons. We suggest a construction of high-order approximations to a controller that guarantees a desired performance level on the basis of the exact decomposition of the full-order Riccati equations to the reduced-order slow and fast equations. This leads to effective asymptotic and numerical algorithms. We show that the high-order accuracy controller improves the performance.