In Lyapunov stability theory, we are studying the dynamical character of dynamical systems without finding the solution of the considered system. But how the existence of a solution is ensured?
Hi,
Yes stability analysis of dynamical nonlineaire systems can be studied by Lyapunov stability theory.
Also please take a look at those links.
https://www.sciencedirect.com/topics/engineering/lyapunov-stability-theory
http://web.tuat.ac.jp/~gvlab/ronbun/ReadingGroupControl/mls-lyap.pdf
https://hal.archives-ouvertes.fr/hal-01634266/document
https://www.inderscience.com/info/ingeneral/forthcoming.php?jcode=ijdsde
Article Stability analysis of the homogeneous nonlinear dynamical sy...
Best regards
A Lyapunov function is a scalar function that can be used to determine the stability of an equilibrium point. The idea behind a Lyapunov function is that it decreases along the solutions of the system, meaning the solutions are attracted towards the equilibrium point. By choosing appropriate Lyapunov functions, the stability of the equilibrium point can be determined.
In general, Lyapunov stability theory is a powerful tool for studying the stability of dynamical systems, and can be used to determine whether an equilibrium point is stable and whether solutions exist. However, it is just a necessary condition for the stability, existence of solution and it does not necessarily guarantee that the solutions are unique or that they will be global (valid for all initial conditions) solutions.
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