On the conditions defining stability nature for some classes of nonlinear dynamic system

The paper shows that stability analysis for some classes of nonlinear dynamic systems of any order enables direct Lyapunov function construction based on the second member of the system's equation. This fact can be used not only for dynamic systems analysis but for their synthesis as well. The conditions determining the stability nature of isolated equilibrium states of autonomous nonlinear dynamic systems of any order are developed; these conditions have clear geometric interpretation. Sufficient and necessary/sufficient conditions for asymptotic stability as well as sufficient conditions for stability and instability are presented.