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In the paper, we consider a two-hyperbolic system with constant coefficients. Control parameters are entered. We note that coefficients depend on the control parameters. We investigate questions of formulation of mixed problems (problems with initial and boundary conditions) for the system. To determine the numerical solution of the mixed problem, we propose an upwind difference scheme of splitting in directions, which depends on the characteristic velocities. We study the issue of stability of the proposed difference scheme in the energy norm.