# Stability analysis other than Lyapunov

Is there a method for stability analysis of nonlinear dynamical systems $$\dot x= f(x)$$, except Lyapunov theory?

• Linearize and determine the eigenvalues of the $$A$$ matrix, which gives local guarantees.
• Determine the fixed points of $$f(x)$$ and analyze whether these are stable by analyzing the Jacobians of the fixed points (also local guarantees)