Constructive Generation and Verification of Lyapunov Functions around Fixed Points of Nonlinear Dynamical Systems
AbstractAn iterative method is developed that provides a transformation of
coordinates of a dynamical system near a fixed point. In the new
coordinates, Lyapunov functions and pseudo-Lyapunov functions can be
determined. Using differential algebraic methods, the transformations
can be chosen to belong to the same symmetry groups as the underlying
motion. For area preserving stable motion, the method yields first
integrals or near-first integrals of motion, and the convergence
properties of the perturbative technique are tied to the question of
integrability of the motion. For other stable motion, the method often
yields Lyapunov functions that can be used to locally assert stability
of the motion. Examples of the use of the method are given.
M. Berz, K. Makino, International Journal of Computer Research 12,2 (2003) 235-244
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