Numerical two-dimensional two-fluid MHD simulations of dynamic magnetosphere-ionosphere (MI) coupling have been performed to model the effects imposed on the auroral ionosphere by a powerful HF radio wave transmitter. The simulations demonstrate that modifications of the ionospheric plasma temperature and recombination due to artificial heating may trigger the ionospheric feedback instability when the coupled MI system is close to the state of marginal stability. The linear dispersion analysis of MI coupling has been performed to find the favorable conditions for marginal stability of the system. The development of the ionospheric feedback instability leads to the generation of shear waves which resonate in the magnetosphere between the heated ionospheric E-region and the strong gradient in the speed at altitudes of 1-2 R_E. The application of the numerical results for the explanation of observations performed by low-orbiting satellites above the high-latitude ionosphere heated with a high power ground-based HF transmitter is discussed.