Dynamics of autonomous systems in the presence of unstable variables

The questions of instability in dynamical systems are investigated using the Lyapunov functions method and method of additional functions. The problem of isolation of unstable coordinates has been considered within the bounds of the coordinate approach, and the conception of a bounded instability playing an important role in the analysis of partial stability has been introduced. The question of applicability of Lyapunov theorems about stability by linear approximation in problems of partial stability has been discussed.