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An linear parameter varying guidance method for the hypersonic phase of a space re-entry vehicle is presented. The suggested guidance scheme, relying on flatness approach, is applied to the non-linear model of the European Atmospheric Re-entry Demonstrator. It is shown that the overall guidance scheme achieves robust stability and performance, even in the presence of entry point kinematics dispersions. The design problem is formulated and solved using a finite set of linear matrix inequalities. Finally, Monte Carlo simulation results are presented to demonstrate the effectiveness of the suggested approach.