H/sub /spl infin//-norms and disturbance attenuation for systems with fast transients

It is shown that for a singularly perturbed system, the H/sub /spl infin// norm of the transfer matrix function tends to the largest of the H/sub /spl infin// norms for the boundary layer system and for the reduced slow model. As an application complementing the results of Pan and Basar (1993, 1994), it is proven that fast transients cannot always be neglected when designing a stabilizing controller with disturbance attenuation.