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The singular perturbation theory developed by Kokotovic et al. is applied to the distributed parameter system described by a set of parabolic differential equations involving a singularly perturbing parameter. The method is shown that gives an asymptotic expansion of the feedback gain matrix by introducing a Riccati-like decoupling and applying a boundary layer method developed in the lumped parameter system. The asymptotic expansion is uniformly valid in the time interval considered. The basic theorem giving the asymptotic accuracy is offered. The results are useful in many fields, e.g., nuclear reactor control with distributed parameters. A numerical example is shown. 17 references.