A global feedback control of a system that exhibits a subcritical monotonic instability
at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero
mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero
mode. The method based on a variational principle is applied for the derivation of a
low-dimensional evolution model. In the framework of this model the investigation of the
system’s dynamics and the linear and nonlinear stability analysis are carried out. The
obtained results are compared with the results of direct numerical simulations of the
original problem.