In this paper,we address the problem of analysing the local stability of the equilibrium um point of uncertain nonlinear systems and estimating its respective domain of attraction. We derive LMI conditions for the local robust stability problem based on Lyapunov functions which are polynomial functions of the state and uncertain parameters. The problem of maximizing the estimation of the domain of attraction consists of maximizing a level surface of the Lyapunov function inside a given polytope. Numerical examples show the performance of our approach.
Uncertain nonlinear systems; linear matrix inequalities; domain of attraction; polynomial Lyapunov functions
