Abstract
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.
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