Optimisation of the Zubov and Ingwerson methods for constructing Lyapunov functions

The Zubov and Ingwerson procedures for constructing Lyapunov functions depend upon an initial choice of some function of the state variables. A direct search procedure is described for obtaining the optimum function, and hence the Lyapunov function of an arbitrary order which gives the best estimate of the region of asymptotic stability. The method is illustrated by an example.