The invention relates to the production and use of block copolymers which are obtained by means of controlled radical polymerization in the presence of nitroxides for the purpose of reinforcing fragile polymer matrices. The invention offers advantages such as (i) simplicity of copolymer synthesis and use and (ii) fine dispersion of the copolymer molecules in the fragile matrix, which ensures both the transparency of the material and high reinforcement against impact. More specifically, the invention relates to the radical synthesis of block copolymers comprising at least three blocks, which include one block having a glass transition temperature of less than 0° C. and a thermoplastic end block having a glass transition temperature of more than 0° C., thereby guaranteeing compatibility with the fragile matrix to be reinforced against impact.