  We investigate the behavior of the Lyapunov spectrum of a linear
discrete-time system under the action of small perturbations in order to obtain
some verifiable conditions for stability and openness of the Lyapunov spectrum.
To this end we introduce the concepts of broken away solutions and splitted
systems. The main results obtained are a necessary condition for stability and
a sufficient condition for the openness of the Lyapunov spectrum, which is
given in terms of the system itself. Finally, examples of using the obtained
results are presented.
