For semilinear control systems the Lyapunov spectrum is approximated via the Floquet and the Morse spectrum. If the semilinear control system possesses singular subspaces, which corresponds to blockdiagonality of the system, it can be shown that the analysis of these two spectra can be reduced to these lower-dimensional systems. The Floquet spectrum of control sets with nonvoid interior is contained in the Floquet spectra of the restricted control systems. The Morse spectrum coincides with the union of the Morse spectra of the restricted systems. In particular, all Lyapunov exponents are attained on the singular subspaces.