The article solves the problem of controlling the mode of complete synchronization of two chaotic systems at different values of their parameters. The control is based on the principle of linear feedback on the phase vector of chaotic generators. The introduction of feedback makes it possible to ensure the equality of the components of the phase vectors of the receiver and the transmitter due to the equality of their Lyapunov characteristic indicators. To change the Lyapunov spectrum, it is proposed to synthesize control by the modal control method based on the solution of the Sylvester linear matrix equation on the basis of the theorem on the topological equivalence of the nonlinear system and its linearized model. An example of using this technique to synchronize the chaotic oscillations of two Lorentz systems when transmitting information using chaotic masking is considered. Computational experiments confirm the operability of the proposed method of ensuring the synchronization of two chaotic systems.