Extension on Rational Functions Using a Bezoutian Approach for the Estimation of the Domain of Attraction for Nonlinear Autonomous Systems

Abstract

One of modern control engineering and system theory key tasks is to investigate and ensure stability for arbitrary given nonlinear systems. There are many methods to ensure stability, but most of them are restricted to a small set of possible functions. This set of functions consists in most cases of quadratic Lyapunov functions (LF). There already exist some methods to remove the constraint for the use of quadratic Lyapunov functions. In this presented article we want to show how a bezoutian approach for the estimation of the domain of attraction (DA) can be extended for arbitrary rational LF that fullfill the Lyapunov conditions. The domain of attraction will be succesfully determined by an upper and lower bound. The exactness of the here presented algorithm can be altered by a reduction of the step size. The estimated lower bound provides us with a guaranteed DA. Two examples, which compare a rational towards a common LF at the end of the article illustrate the results of this work.