Feedback control of two-dimensional (2-D) systems is a problem of considerable importance in both theory and practical applications. In this paper, we present a state-space solution to the problem of H-infinity control of 2-D systems. For a linear discrete time 2-D system described by a 2-D state-space Roesser model, a 2-D dynamic output feedback controller is designed to achieve the closed-loop system asymptotic stability and a specified H-infinity performance using a linear matrix inequality (LMI) approach. We further give a solution for robust stabilization of 2-D systems subject to a class of norm bounded uncertainties. The results are demonstrated by an application example of stabilization of processes expressed in a Darboux equation.