Generalisation of Zubov´s construction procedure for Lyapunov functions

This letter presents a method by which Lyapunov functions can be generated for an n-dimensional nonlinear system. Recursive relationships are derived for the coefficients of a multidimensional power series which are a generalisation of the results of Margolis and Vogt. The solutions for the higher-order coefficients of the series incorporate some useful extensions of the concept of Kronecker matrix products.