Robust stability and domain of attraction of uncertain nonlinear systems

This paper deals with the robust stability of nonlinear systems having real time varying parameters with magnitude and rate of variation which are confined to a given polytope. The system matrices may have entries which are rational functions of the states and uncertain parameters. We present LMI conditions that, when feasible, guarantee the asymptotic stability of the origin of the system through a Lyapunov function of the type v(x, δ)=x´P(x, δ)x where P(x, δ) is a polynomial matrix function of the states (x) and uncertain parameters (δ). A method of maximizing an estimate of the region of attraction is also presented