Estimating Minimal Domains of Attraction for Uncertain Nonlinear Systems

In this article, we investigate the inner estimations of the minimal domains of attraction (MDA) for uncertain nonlinear systems, whose uncertainties are modeled by parameters defined in a semialgebraic set. We begin from an initial inner estimation of MDA and then enlarge this initial inner estimation by iterative calculating common Lyapunov-like functions with a linear sum of squares programming-based approach. Afterwards, this enlarged inner estimation of MDA is further improved by iterative computations of parameter-dependent Lyapunov-like functions. Especially, we use a simple semialgebraic set, described by a polynomial level-set function, to under-approximate this improved estimation. In the end, our methods are implemented and tested on several uncertain examples with comparisons to existing methods in the literatures.