A closed-form solution for a terminal cost problem is obtained for synthesizing suboptimal control of nuclear reactors with spatially distributed parameters by using the Sylvester theorem. The inverse of the neutron velocity is regarded as a small singular parameter, and the model, adopted for simplicity, is a cylindrically symmetrical reactor. The Helmholtz mode expansion is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter systems. The explicitly obtained control is particularly convenient for machine calculation to any degree of precision.