Stability region analysis for uncertain nonlinear systems

We propose a method to compute provably invariant subsets of the region-of-attraction for the asymptotically stable equilibrium points of uncertain nonlinear dynamical systems. We consider uncertainties that can be modeled as perturbations to a nominal system where perturbations obey polynomial bounds on semialgebraic sets containing the equilibrium point. The main computational tool is the sum-of-squares optimization.