The article deals with linear homogeneous stationary systems of second-order differential equations that have the property of exponential stability. It is found out for which set of such systems, corresponding to a bounded domain in a two-dimensional space of acceptable parameters, the value of overshoot can be calculated as the ratio of the maximum and minimum eigenvalues of the Lyapunov matrix. This method can be useful in solving problems of applied mathematics and control processes. To determine the approximate location of the desired area, the overshoot value was calculated using a method that can be applied to a wider class of systems. In the course of work, no systems with the necessary properties were defined, so the method requires further development.