On the Lyapunov and Bohl exponent of time-varying discrete linear system

This note studies the problem of bounds for the Lyapunov exponent of a parameter perturbed system when the perturbation has finite average value. Such a bound is presented in terms of Bohl exponent of the unperturbed system. In particular, it has been shown that the Lyapunov exponent of perturbed system is not greater than the Bohl exponent of the unperturbed system if the average value of perturbations is zero. The obtained result is illustrated by a numerical example.