On the property of proportional local assignability of the Lyapunov spectrum for discrete time-varying systems

We investigate the question of the proportional local assignability of the Lyapunov exponents of every system belonging to the Bebutov hull of a given linear control system with discrete time. We have obtained conditions that ensure the equivalence of the uniform complete controllability of a given system and the proportional local assignability of the Lyapunov spectrum of each system from the Bebutov hull of this given system.