Possible Values of the Measure of Perron Stability of Linear Differential Systems

In this paper, we consider the situation when some of the perturbed solutions (which could form an arbitrary but essential part of all the solutions) with the initial values close enough to the point of equilibrium do not remain close to that point but return back to it at arbitrarily late times instances. Such a situation can be described with the use of the special characteristics that is the measure of Perron stability, for which the possible range of values if found in the paper.