Estimation of the Domain of Attraction for Uncertain Nonlinear Autonomous Systems via rational Lyapunov functions: A Bezoutian Approach

In todays modern control engineering and system theory, the investigation of stability for arbitrary nonlinear systems is one of the central topics. Numerous different methods established in recent years, but most of them are limited to a small set of possible functions. The main purpose of this contribution is, to present a method for the approximation of the robust domain of attraction (RDA) for uncertain polynomial systems using rational instead of common quadratic Lyapunov functions (LF). We consider a polynomial system where the uncertainty is given by a polynomial mapping of an interval into the uncertainties. We use a bezoutian algorithmic approach for the estimation of the RDA. This algorithm successfully provides us with an enclosure of the RDA. The effectiveness of the technique is illustrated by some examples.