In this paper, we consider the problem of robust H-infinity control for a class of uncertain nonlinear systems. We derive LMI conditions for analyzing regional stability and performance based on Lyapunov functions which are polynomial functions of the state and uncertain parameters. More specifically, we provide an energy bound on the input disturbance which guarantees that the state of the system stays inside a given region. For the given bound on the input disturbance, we also minimize the L2-gain of the input-output operator. Through an iterative algorithm, the proposed technique is applied to control systems. Numerical examples are presented to illustrate our results.