Well, imagine there is a country called Hegemonistan, and it has the most power economically and politically at the moment. A large plurality at least.

Now define the change in stability between t0 and t1 as something like inversely proportional to the weighted average of changes in relative power rankings among countries.

By definition, maintaining stability will tend to keep Hegemonistan in its power positions. And vice versa.

So, stabilization is roughly identical to helping Hegemonistan.