On assignability of Lyapunov spectrum of discrete linear time-varying system with control

In this paper we study discrete linear time-varying system with control and bounded coefficients. For such systems we consider problems of the proportional global assignability and proportional local assignability of the Lyapunov spectrum of the discrete linear time-varying system with control. This is a generalization of the pole placement theorem, which is well-known in the theory of time-invariant system. The main results present sufficient conditions for considered types of assignability.