Stability region estimation for systems with unmodeled dynamics

We propose a method to compute invariant subsets of the robust region-of-attraction for the asymptotically stable equilibrium points of systems with polynomial nominal vector fields and unmodeled dynamics. The effects of unmodeled dynamics are accounted for as systems satisfying certain gain relations or dissipation inequalities. The methodology is extended to systems with parametric uncertainties and an informal branch-and-bound type refinement procedure to reduce the conservatism is discussed. We demonstrate the method on a polynomial approximation of uncertain controlled short period aircraft dynamics.