Construction of Lyapunov Functions for Nonlinear Systems Using Normal Forms*

In w8x, the authors used normal form theory to construct Lyapunov functions for critical nonlinear systems in normal form coordinates. In this work, the authors expand on those ideas by providing a method for constructing the associated normal form transformations that gives rise to the systematic development of a method for constructing Lyapunov functions for critical nonlinear systems in their original coordinates.